STAT 170 Ch 9 guided notes

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STAT 170 Ch 9 - Inferring Population Means Chapter 9 Topics • Apply the Central Limit Theorem for sample means • Make inferences about population means using confidence intervals and hypothesis tests Section 9.1 Sample Means of Random Samples • Discuss the Accuracy and Precision of the Sample Mean as an Estimate of the Population Mean • Find the Standard Error of the Sampling Distribution of the Sample Mean Three Characteristics of the Sample Mean Notation Review: μ = population mean σ = population standard deviation s = sample standard deviation x = sample mean Accuracy and Precision of the Sample Mean The ______________________ of an estimator is measured by the bias , and the ______________________ is measured by the standard error .  The sample mean is unbiased when estimating the population mean – on average, the sample mean is the same as the population mean.  The precision of the sample mean depends on the variability in the population. The more observations we collect, the more precise the sample mean becomes. Sampling Distribution of the Sample Mean The sampling distribution can be thought of as the distribution of _________________________________________ that would result from drawing repeated samples of a certain size from the population.  Reminder: The standard deviation of the sampling distribution is called the standard error . Example: The response time for the population of all emergency calls to a fire department between 2013 and 2016. It is right-skewed with a mean response time of 6.3 minutes and a standard deviation of 2.8 minutes . Take a simulation that involves a random sample of 50 observations from the data set and calculate the average response time. Repeat this simulation many times: 1. What is the typical value of the sample mean? 2. If unbiased, how far is it from 6.3 minutes?

Effect of Sample Size on the Sampling Distribution As the sample size _________________ the standard error ___________________ but the mean remains the _____. Accuracy and Bias of the Sample Mean For all populations, the sample mean, if based on a _______________ sample, is _______________ when estimating the population mean. The standard error of the sample mean is As the sample size increases, the sample mean becomes more ______________. Example : Playlists A student has a large digital music library. The mean length of the songs is 258 seconds with a standard deviation of 87 seconds. The student creates a playlist that consists of 30 randomly selected songs. a. Is the mean value of 258 seconds a parameter or a statistic? Explain. b. What should the student expect the average song length to be for his playlist? c. What is the standard error for the mean song length of 30 randomly selected songs? In-Class Engagement 1. A study of all the students at a small college showed a mean age of 20.7 and a standard deviation of 2.5 years. a. Are these number statistics or parameters? Explain. b. Label both numbers with their appropriate symbol. 2. Drivers in Alaska drive fewer miles yearly than motorists in any other state. The annual number of miles driven per licensed driver in Alaska is 9134 miles. Assume the SD is 3200 miles. A random sample of 100 licensed drivers in Alaska was selected and the mean number of miles driven yearly for the sample was calculated. a. What value would we expect for the sample mean? b. What is the standard error for the sample? What does this mean? Your Turn 1. A survey of 100 random full-time students at a large university showed the mean number of semester units that students were enrolled in was 15.2 with a standard deviation of 1.5 units. a. Label the numbers with their appropriate symbol.

2. The average shower in the US lasts 8.2 minutes. Assume the standard deviation of 2 minutes. a. Do you expect the shape of the distribution of shower lengths to be normal, right-skewed, or left-skewed? Explain. b. Suppose we survey a random sample of 100 people to find the length of their last shower. We calculate the mean length from the sample and record the value. We repeat this survey 500 times. What will be the shape of the distribution of these sample means? c. Refer to part b. What will be the mean and the standard deviation of the distribution of these sample means? Section 9.2 Central Limit Theorem for Sample Means • Apply the Central Limit Theorem for Sample Means to Calculate Probabilities • Describe the Features of the t -distribution Central Limit Theorem for Sample Means If certain conditions are met, the Central Limit Theorem assures us that the distribution of sample means follows an approximately ___________________ distribution no matter what the shape of the population distribution. *Note: If the population is Normally distributed, then the sampling distribution is normally distributed, regardless of the sample size. Conditions to Check When determining whether you can apply the Central Limit Theorem to analyze data, consider these three conditions: 1. _______________ Sample and _____________________________ . Each observation is collected randomly from the population and observations are independent of each other. 2. ____________ sample . Either the population distribution is Normal or the sample size is large. (usually 25 is large enough). 3. _________ population . If the sample is collected without replacement then the population must be at least 10 times larger than the sample size. If the three conditions are met, then the sampling distribution of _________________________________________ is approximately Visualizing Distributions of the Sample Mean The figure to the right shows the distribution of in-state tuition and fees for all two-year colleges in the United States for the 2012-2013 academic year. Note that it is skewed and multimodal.

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These figures show the distribution of the sample mean for samples of size 30 and size 90 drawn from the skewed multimodal distribution on the previous page. Note the shape of each is approximately _____________________ and the standard error ___________________ as the ______________________________ increases. Example: Weights of 10-Year-Old Boys According to data from the National Health and Nutrition Exam Survey, the mean weight of 10-year-old boys is 88.3 pounds with a standard deviation of 2.06 pounds. Assume the distribution of weights is Normal. a. Suppose we take a random sample of 30 boys from this population. Can we find the approximate probability that the average weight of this sample will be above 89 pounds? If so, find it. If not, explain why. b. Suppose we take a random sample of 10 boys from this population. Can we find the approximate probability that the average weight of this sample will be above 89 pounds? If so, find it. If not, explain why not. Example: Home Prices Home prices in a certain community have a distribution that is skewed right. The mean of the home prices is $498,000 with a standard deviation of $25,200. a. Suppose we take a random sample of 30 homes in this community. What is the probability that the mean of this sample is between $500,000 and $510,000? b. Suppose we take a random sample of 10 homes in this community. Can we find the approximate probability that the mean of the sample is more than $510,000? If so, find it. If not, explain why not.

Identify the Distribution There are three distributions below. One of these distributions is a population. The other two distributions are approximate sample distributions of the sample means randomly sampled from the population, one of sample size 10 and the other of sample size 25. Match the graph with the correct distribution. Your Turn 1. Some sources report that the weights of full-term newborn babies have a mean of 7 pounds and a standard deviation of 0.6 pounds and are normally distributed. a. What is the probability that one newborn baby will have a weight within 0.6 pound of the mean? b. Explain why the sampling distribution of sample means with sample size 4 is normally distributed. c. What is the probability the average of four babies’ weights will be within 0.6 pound of the mean? d. Explain the difference between (a) and (c). 2. Some sources report that the weights of full-term newborn babies have a mean of 7 pounds and a standard deviation of 0.6 pounds and are normally distributed. In the given outputs, the shaded areas (reported as p=) represent the probability that the mean will be larger than 7.6 or smaller than 6.4. One of the outputs uses a sample size of 4 and one uses a sample size of 9. a. Which is which, and how do you know? b. These graphs are made so they spread out to occupy the room on the face of the calculator. If they had the same horizontal axis, one would be taller and narrower than the other. Which one would that be, and why?

3. Maryland has one of the highest per capita income in the US, with an average income of $75,847. Suppose the standard deviation is $32,000 and the distribution is right-skewed. A random sample of 100 Maryland residents is taken. a. Is the sample size large enough to use the CLT for means? Explain. b. What would be the mean and standard error for the sampling distribution? c. What is the probability that the sample mean will be more than $3200 away from the population mean? The t -Statistic Hypothesis tests and confidence intervals for estimating and testing the mean are based on a statistic called the t -statistic: Since the population standard deviation is almost always unknown , we divide by an _______________ of the _________________________, using the sample standard deviation s instead of σ . The t -Distribution The t -statistic does not follow the Normal distribution, because the denominator ______________________ with every sample size. The t -statistic is more variable than the z -statistic, whose denominator is always the _____________. If the three conditions for using the Central Limit Theorem hold, the t -statistic follows a distribution called the t -distribution . The __________________________________ (_______) represent how many values involved in a calculation have the freedom to vary. The t -Distribution is  Symmetric and “bell-shaped”  Has thicker tails than the Normal distribution  Shape depends on the degrees of freedom ( df )  If df is small, the tails are thick; as d f increases, tails get thinner If the three conditions for using the Central Limit Theorem hold, the t-statistic follows a distribution called the t -distribution . When small sample sizes were used to make inferences about the mean , even if the population was Normal, the Normal distribution just didn’t fit the results that well. The t -distribution turned out to be a better model than the Normal for the sampling distribution of x when _______________________ ___________________________________________.

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The t -distribution’s _________________ depends on only one parameter, called the degrees of freedom (df).  The number of degrees of freedom is (usually) an integer: 1, 2, 3, and so on. If the df is small, then the t -distribution has very ________________ tails.  As the degrees of freedom get larger, the tails get ________________.  Ultimately, when the df is infinitely large, the t -distribution is exactly the same as the N(0, 1) distribution. Below, we have the t -distributions with 1, 10, and 40 degrees of freedom. In each case, the t-distribution is shown with an N(0, 1) curve so that you can compare them. (We compare to the N(0, 1) because it is familiar and because, as you can see, the t-distribution and the Normal distribution are very similar.) Normal or T-Distribution? When should you use a normal distribution for the sampling distribution, and when should you use a t -distribution? • Use normal distribution when the population standard deviation is known. • Either: the population has to be normally distributed • Or: the sample size is larger than 25 • Use t -distribution when • Either: population standard deviation is unknown • Or: the sample size is small (under 25) *Note: If pop SD ( σ ) is not known, use t regardless of sample size In-Class Engagement 1. The mean age of all 118 used Toyota vans for sale was 3.1 years with a standard deviation of 2.7 years. The distribution of ages is right-skewed. For a statistics project, a student randomly selects 35 vans from this data set and finds the mean of the sample is 2.7 years with a SD of 2.1 years. a. Find each of these values: μ,σ , x, ∧ s b. Which of the values listed in part a are parameters? Which are statistics? c. Are the conditions for using the CLT fulfilled? What would be the shape of the approximate sampling distribution of a large number of means, each from a sample of 35 vans?

Your Turn The average income in Connecticut in 2013 was $60,000 per person per year. Suppose the standard deviation is $30,000 and the distribution is right-skewed. a. Why does it make sense that the distribution of income is right-skewed? Suppose we take a random sample of 400 residents of Connecticut. We want to find the probability that the sample mean will be more than $3000 away from the population mean. The output is shown: a. Why is the distribution normal and not right-skewed like the population? b. Why is the z score 2? c. What is the probability that the sample mean will be more than $3000 away from the population mean? Section 9.3 Answering Questions About the Mean of a Population  Construct and Interpret a Confidence Interval for a Population Mean Answering Questions About the Mean of a Population There are two approaches for answering questions about a population mean: 1. Confidence intervals – Used for estimating parameter values 2. Hypothesis tests – Used for deciding whether a parameter’s value is one thing or another These are the same methods as introduced in previous chapters for population proportions but modified to work with population means. Confidence Interval  Provides a _________________________________________ for the _________________________ mean along with a measure of the uncertainty in our estimate  Is a measure of the uncertainty in our estimate – the higher the level of confidence, the better our confidence interval performs When to Use Confidence Intervals  Use confidence intervals whenever you are ____________________ the value of a _____________________ on the basis of a ___________________ sample.  Do Not use a confidence interval if there is no uncertainty in your estimate. If you have data for the entire population you don’t need to find a confidence interval since the population parameter is known – there is no need to estimate it.

Confidence Interval for a Population Mean: Conditions Before constructing a confidence interval for a population mean, check these three conditions: 1. Random, independent sample 2. Large sample – Either the population is Normally distributed or the sample size is at least 25. 3. Big population – If the sample is collected without replacement the population must be at least 10 times larger than the sample size. Example: Car Prices A used car website wanted to estimate the mean price of a 2012 Nissan Altima. The site gathered data on a random sample of 30 such cars and found a sample mean of $16,610 and a sample standard deviation of $2736. The 95% confidence interval for the mean cost of this model car based on this data is (15588, 17632) a. Describe the population. Is the number $16,610 an example of a parameter or a statistic? b. Verify that the conditions for a valid confidence interval are met. Interpretation of the Confidence Level The confidence level is a measure of how well the method used to produce the confidence interval performs. Example A 95% confidence interval means that if we were to take many random samples of the same size from the same population, we expect 95% of them would “work” (contain the population parameter) and 5% of them would be “wrong” (not contain the population parameter). *Note: Confidence levels are NOT ______________________________ Calculating the Confidence Interval General structure: where and Because we usually do not know the population standard deviation, we replace SE with its estimate that uses the sample standard deviation. One-Sample t -Interval The one-sample t -interval is a confidence interval for a population mean. Where and The multiplier t* is found using the t -distribution with n−1 degrees of freedom.

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To construct a one-sample t -interval you need four pieces of information: 1. The sample mean, _____, that you calculate from the data. 2. The sample standard deviation, ______, which you calculate from the data. 3. The sample size, ______ . 4. The multiplier, ______, which you can look up in a table or use technology. t* is determined by the confidence level and the sample size. The value of t* tells us how wide the margin of error is, in terms of standard errors. For example, if t* = 2, then our margin of error is 2 standard errors wide. Finding t * _________can be found using a t -distribution table, but because most tables stop at 35 or 40 degrees of freedom, it is best to use technology to construct confidence intervals. Example: Highway Speeds Data on the speed (in mph) for random sample of 30 cars traveling on a highway was collected. The mean speed was 63.3 mph with a standard deviation of 5.23 mph. a. Find the 95% confidence interval for the mean speed of all cars traveling on the highway. Verify that the necessary conditions hold. Using the TI-84 Calculator To construct a confidence interval for a population mean on the T I-84 calculator: 1. Push STAT > TESTS then select T-INTERVAL . 2. If you  have data in a list, select DATA . Enter the name of the list where the data is stored, leave Freq: 1, select your C-level and press Calculate .  do not have data in a list, select STATS . Enter the sample mean, standard deviation, sample size. Select your C-level and press Calculate . b. Interpret the interval. c. Is it plausible that the mean speed of cars on the highway is 67 mph? Why or why not? Example: Movies A random sample of 35 college students was asked how many movies they had seen in the previous month. The sample mean was 4.14 movies with a standard deviation of 10.02. a. Construct a 90% confidence interval for the mean number of movies college students see per month. b. If we were to use the data to construct the 95% confidence interval, would the interval be wider or narrower than the 90% confidence interval?

c. What would be the effect of taking a larger sample on the width of the interval? In-Class Engagement The acceptance rate for a random sample of 15 medical schools in the US was taken. The mean acceptance rate for this sample was 5.77 with a standard error of 0.56. Assume the distribution of acceptance rates is normal. a. Decide whether each of the following statements is worded correctly for the confidence interval. Fill in the blanks for the correctly worded one(s). Explain the error for the ones that are incorrectly worded. i. We are 95% confident that the sample mean is between ______ and _____. ii. We are 95% confident that the population mean is between _____ and _____. iii. There is a 95% probability that the population mean is between ____ and _____. b. Based on your confidence interval, would you believe the average acceptance rate for medical schools is 6.5? Explain. A statistics instructor randomly selected four bags of oranges, each bag labeled 10 pounds, and weighed the bags. They weighed 10.2, 10.5, 10.3, and 10.3 pounds. Assume that the distribution of weights is normal. a. Find a 95% confidence interval for the mean weight of all bags of oranges. Use technology for your calculations. b. Does the interval capture 10 pounds? Is there enough evidence to reject the null hypothesis that the population mean weight is 10 pounds? Explain your answer. Your Turn A random sample of 10 colleges from Kiplinger’s 100 Best Values in Public Education was taken. The mean rate of graduation within four years was 43.5% with a margin of error of 6.0%. The distribution of graduation rates is normal. a. Interpret the confidence interval. a. Can you reject a population mean percentage of 50% on the basis of these numbers? Explain.

The weights of four randomly chosen bags of horse carrots, each bag labeled 20 pounds, were 20.5, 19.8, 20.8, and 20.0 pounds. Assume that the distribution of weights is normal. Find a 95% confidence interval for the main weight of all bags of carrots. a. Interpret the confidence interval. a. Can you reject a population mean of 20 pounds? Explain. A researcher collects one sample of 27 measurements from a population and wants to find a 95% confidence interval. a. Should the researcher use the normal or t- distribution? Why? b. What value should he use for z* or t* ? Section 9.4 Hypothesis Testing for Means  Conduct a Hypothesis Test for a Population Mean Four Steps for Hypothesis Testing 1. Hypothesize. State your hypotheses about the population parameter. 2. Prepare. Test statistic, check conditions and assumptions. 3. Compute to Compare. Choose a significance level and compute a test statistic and p -value. 4. Interpret. Do you reject the null hypothesis or not? What does this mean? Hypothesis Test: Claim About a Population Mean Test Statistic for a One-Sample t -Test: where If conditions hold, the test statistic follows a t -distribution with _____________________. Two Conditions: 1. Random, independent sample 2. Large sample: The population must be Normal or the sample size must be at least 25. Example: Nursing In 2010, the mean years of experience among a nursing staff was 14.3 years. A nurse manager took a survey of a random sample of 35 nurses at the hospital and found a sample mean of 18.37 years with a standard deviation of 11.12 years. Do we have evidence that the mean years of experience among the nursing staff at the hospital has increased? Use a significance level of 0.05.

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Using the TI-84 Calculator To conduct a hypothesis test for a mean with one population on the T I-84 calculator: 1. Push STAT > TESTS then select the T-test option.  If your data is in a list, select DATA, enter the number in H 0 , the list the data is in. Leave Freq at 1, and highlight the sign in your H 0  If you have summary statistics, select STATS and enter the required statistics. 3. Press Calculate or Draw . The test statistic and p -value will be displayed. Using StatCrunch Stats > t Stats > One Sample > With Summary One- and Two-Sided Alternative Hypotheses Just as with hypothesis tests for proportions, hypothesis tests can be one-sided or two-sided depending on the research question. The choice of the alternative hypothesis determines how the p -value is calculated. Example: Hockey Attendance In the 2010 season, average home attendance for NHL hockey games was 17,072. Suppose a sports statistician took a random sample of 30 home hockey games during the 2014 season and found a sample mean of 18,104 with a standard deviation of 1203.5. Can we conclude that mean attendance at NHL games has changed since the 2010 season? In-Class Engagement The US Department of Health has suggested that a healthy total cholesterol measurement should be 200 mg/dL or less. Records from 50 randomly and independently selected people from the NHANES study showed the results: Test the hypothesis that the mean cholesterol level is more than 200 using a significance level of 0.05. Assume that conditions are met. A body mass index (BMI) of more than 25 is considered unhealthy. The Minitab output given is from 50 randomly and independently selected people from the NHANES study.

Test the hypothesis that the BMI is more than 25 using a significance level of 0.05. Assume that conditions are met. Your Turn In the US, the population mean height for 3-year-old boys is 38 inches. Suppose a random sample of 15 non-US 3- year-old boys showed a sample mean of 37.2 inches with a standard deviation of 3 inches. The boys were independently sampled. Assume that heights are normally distributed in the population. a. Determine whether the population mean for non-US boys is significantly different from the US population mean. Use a significance level of 0.05. b. Now suppose the sample consists of 30 boys instead of 15, and repeat the test. c. Explain why the t -values and p-values for parts a and b are different. Section 9.5 Comparing Two Population Means  Conduct Hypothesis Tests and Construct Confidence Intervals About a Population Mean for Independent and Dependent Samples Independent versus. Dependent Samples When comparing two populations, it is important to note whether the data are two __________________________ samples or are _________________________________________ samples. Paired/Dependent Samples Each observation in one group is coupled or paired with one particular observation in the other group. Examples:  “Before and after” comparisons  Related objects/people (twins, siblings, spouses) Example: Dependent or Independent? People chosen in a random sample are asked how many minutes they spend reading and how many minutes they spent exercising during a certain day. Researchers wanted to know how different the mean amounts of time were for each activity. Is this a dependent or an independent sample? A sample of men and women each had their hearing tested. Researchers wanted to know whether, typically, men and women differed in their hearing ability. Is this a dependent or an independent sample?

A random sample of married couples are asked how many minutes per day they spent exercising. Means were compared to see if the mean exercise times for husbands and wives differed. Confidence Intervals: Independent Samples To construct the confidence interval for the difference in population means given independent samples, check three conditions: 1. Random samples and independence – Both samples are randomly taken from their populations and each observation is independent of any other. 2. Independent samples – The samples are not paired. 3. Large samples – The populations are approximately Normal or the sample sizes are each 25 or more. General structure: Specifically: The estimate of difference = Two-Sample t -Interval: ______ is based on an approximate t -distribution with _______ as the smaller of _________ and _________. For more accuracy, use technology. Interpreting Confidence Intervals Independent samples ______________________ Interpreting confidence intervals for the difference of population means given independent samples is the same as interpreting confidence intervals for the difference of population proportions. 1. If 0 is in the interval, there is no significant difference between _______ and ______ 2. If both values in the confidence interval are positive, then _________________ 3. If both values in the confidence interval are negative, then ________________ Example: Units A college randomly surveyed day students and evening students to determine the number of units students were enrolled in. The data is shown in the table. Use the data to find a 95% confidence interval for the difference in the mean difference in number of units for the two groups. Based on your confidence interval, is there a difference in mean number of units taken by day and evening students at this college? n mean s Day 72 8.7 3.1 Evening 68 5.9 3.7

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Example: Home Prices in Albuquerque Data on the selling price (in hundreds of $) was obtained for a sample of homes in Albuquerque, New Mexico. Homes were classified as located in the northeast (N E) section of the city or in another location in the city. The data are shown in the table to the right. Construct a 95% confidence interval for the difference in mean home price between the N E section and other sections in the city. Is there a difference in home prices? Hypothesis Testing: Two Means 1. Hypothesize 2. Prepare 1. Random samples, independent observations 2. Independent samples 3. Both populations are approximately Normal or both sample sizes are at least 25 or more. 3. Compute to Compare t = _____ usually says the difference is 0, and 4. Interpret Compare the p -value to the significance level. If the p -value is less than or equal to α , we reject the null hypothesis. Note About Pooling When using technology for a two-sample t -test, use the ______________________ version. It is more accurate in most situations than the pooled version. Example: Units – Hypothesis Test Use the units data to test the claim that the mean number of units taken by day and evening students at the college are different. 1. Hypothesize 2. Prepare 3. Compute to Compare Use technology to compute the test statistic and p -value. 4. Interpret n mean s NE 39 972.8 320.4 other 78 1107.4 401.5 n mean s Day 72 8.7 3.1 Evening 68 5.9 3.7

Using the TI-84 Calculator To run a hypothesis test for the difference of population means (independent samples) on the TI-84 calculator: 1. Push STAT > TESTS then select option 2-SAMP T Test . 2. Select DATA (if you have data in a list) or STATS (if you have summary stats) 3. Enter the sample means, sample standard deviations, and sample sizes as prompted by the calculator, enter the sign in ______ and calculate. Example: Home Prices in Albuquerque – Hypothesis Test Use the data on home prices in Albuquerque to test the claim that the mean price of homes in the NE differs from other areas of the city. Use a significance level of 0.05. 1. Hypothesize 2. Prepare 3. Compute to Compare 4. Interpret Dependent Samples  Transform the original data from two variables into a single variable that contains the _________________ between the scores in Group 1 and Group 2.  After the differences have been computed, we can apply either a confidence interval approach or a hypothesis test approach to the differences. Example: Reading Intervention Suppose 4 th grade children are exposed to a reading intervention program designed to improve scores on a reading assessment. Children were given a pre-test and post-test before and after the reading intervention and the scores are shown in the table below. Assume that all conditions needed to construct the confidence interval are met. Construct a 95% confidence interval for the mean difference in reading score after participating in the program. Based on your confidence interval, do you believe the reading program is effective? Use the reading pre/post data to conduct a hypothesis test to see if there was a difference in mean pre/post-test scores after the reading intervention. Assume the conditions for conducting a hypothesis test are met. Use a 0.05 significance level. 1. Hypothesize 3. Prepare 4. Compute to Compare Pre 10 14 21 18 15 16 18 19 20 25 16 Post 12 14 23 19 21 20 19 21 20 24 16

4. Interpret In-Class Engagement State whether each situation has independent or paired (dependent) samples.  A researcher wants to know whether pulse rates of people go down after brief meditation. She collects the pulse rates of a random sample of people before meditation and then collects their pulse rates after meditation.  A researcher wants to know whether professors with tenure have fewer posted office hours than professors without tenure do. She observes the number of office hours posted on the doors of tenured and untenured professors.  A research wants to compare food prices at two grocery stores. She purchases 20 items at Store A and finds the mean and the SD for the cost of the items. She then purchases 20 items at Store B and again finds the mean and the SD for the cost of the items.  A student wants to compare textbook prices at two bookstores. She has a list of textbooks and finds the price of text at each of the two bookstores. The table shows the output for a two-sample t -test for the number of TVs owned in households of random samples of students at two different community colleges. Each individual was randomly chosen independently of the others; the students were not chosen as pairs or in groups. One of the schools is in a wealthy community (MC), and the other (OC) is in a less wealthy community. Test the hypothesis that the population means are not the same, using a significance level of 0.05. Your Turn Triglycerides are a form of fat found in the body. Carry out a hypothesis test to determine whether men have a higher mean triglyceride level than women. Use a level of significance of 0.05. A random sample of 14 college women and a random sample of 19 college men were separately asked to estimate how much they spent of clothing in the last month. The table shows the data. Test the hypothesis that the population mean amounts spent on clothes are different for men and women. Use a significance level of 0.05. Assume that the distributions are normal enough for us to use the t-test. n mean SD SE OC 30 3.70 1.49 0.27 MC 30 3.33 1.49 0.27 Sex n mean SD SE female 44 84.4 40.2 6.1 male 48 139.5 85.3 12 sex $ sex $ sex $ sex $ sex $ M 175 F 200 M 200 M 200 F 80 F 200 M 100 F 250 M 80 M 50 M 150 M 100 F 150 M 100 M 100 F 200 F 200 M 100 M 120 M 30 F 100 M 200 M 0 M 80 F 20 F 100 M 200 F 80 M 25 F 50 M 60 F 100 F 350

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STAT 170 Ch 9 guided notes

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