M5 Problem Set

d) Suppose this is a representative sample of births in a given year at Johns Hopkins. Suppose, instead of a sample of seven values, we have a sample of 100 birth weights. How should the mean, median, and standard deviation of this sample compare to the same statistics for the sample of seven birth weights?

What do you mean by Sample Variance, Sample Standard Deviation,and Standard Error?

The recent average starting salary for new college graduates in computer information systems is $47,500. Assume salaries are normally distributed with a standard deviation of $5200. a. What is the probability of a randomly selected new graduate receiving a salary between $47,000 and $50,000 (to 4 decimal places)? A b. What is the probability of a randomly selected new graduate getting a starting salary in excess of $50,000 (to 4 decimal places)? c. What percent of starting salaries are no more than $46,000 (to 4 decimal places)? d. The bottom 5% of starting salaries are below what value (to 2 decimal places with no commas)? $ e. The top 3% of the starting salaries are above what value (to 2 decimal places with no commas)? $ A/

Suppose that SAT scores among U.S. college students are normally distributed with a mean of 500 and a standard deviation of 100. What is the probability that a randomly selected individual from this population has an SAT score between 500 and 600? 0.1587 0.3173 0.4207 0.3413

In your own words, describe what the difference is between an error term and a residual. How does sample size affect the variance of each?

QUESTION 28 "For a population with a mean = 440 and a standard deviation = 110, what is the X value corresponding to z = 2.67? (Be sure to round answer to the second decimal place)."

A simple random sample of 8 employees of a corporation provided the following information. Employee Age Gender 1 2 3 21 37 26 W M W 4 5 6 7 8 44 48 50 25 22 W W M M M (a) Determine the point estimate for the average age of all employees. (b) What is the point estimate for the standard deviation of the population? (Round your answer to four decimal places.) (c) Determine a point estimate for the proportion of all employees who are female.

Question 3 Saved 4) Listen A customer service team receives an average of 376 emails every day. Assume that the standard deviation for the number of emails is 96 emails. A random sample of 40 days was selected. a. What is the expected value of the sample mean? b. What is the standard deviation of the sample mean? Round your answer to two decimal places (e.g. 2.12). c. What is the probability that the average number of emails received was between 360 and 372? Round your answer to two decimal places with a leading zero (e.g. 0.18).

Suppose it is known that in a certain large human population cranial length is approximately normally distributed with a mean of 185.6 mm and a standard deviation of 12.7 mm. A random sample of size 10 from this population will have a mean greater than 190 with a=0.05 ? let Z-tabulate = 1.96 and T-tabulate= 2.30

You survey 5 members of a college class about how many hours they study each week: 12 hours, 18 hours, 7 hours, 3 hours, and 15 hours. The class has a total of 28 students. Based on the findings from the 5 students you interviewed, what is the standard deviation for the entire class? What is the range of hours you can expect students to study based on one standard deviation? (Hint: Think Normal Distribution Curve).

The average expenditure on Valentine's Day was expected to be $100.89 (USA Today, February 13, 2006). Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 44 male consumers was $137.38, and the average expenditure in a sample survey of 35 female consumers was $65.11. Based on past surveys, the standard deviation for male consumers is assumed to be $35, and the standard deviation for female consumers is assumed to be $12. The z value is 2.576. Round your answers to  decimal places. b. At 99% confidence, what is the margin of error?  c. Develop a 99%  confidence interval for the difference between the two population means.

2) You work for the FTC. A manufacturer of detergent claims that the mean weight of detergent is at least 6.5 lb. You take a random sample of 64 containers. You calculate the sample average to be 6.43 lb. with a standard deviation of .14 lb. At the 0.02 level of significance, is the manufacturer correct?

For a population with a mean of 75 and a standard deviation of 12, what proportion of sample means of size n = 16 fall below 82?

A sample of n = 16 scores has a mean of M = 56and a standard deviation of s = 12 . a. Explain what is measured by the sample standard deviation. b. Compute the estimated standard error for the sample mean and explain what is measured by the standard error.

4.33 124 For a population of 1000 items, μ = 50 and o= 10. What is the mean and standard error of the theoretical sampling distribution of the mean for sample sizes of (a) 25 and (b) 81? Ans. (a) x = 50 units and ox= 2 (b) μx = 50 units and ox = 1.07 XX1. +1₁ f+h f th 10 if th

I'm assuming for this problem I need to find the z-score first then find the value on the distribution chart?The mean number of calories consumer per day for females aged 27 is 2725 with a standard deviation of 277. If a simple random sample of 100 females is selected, what is the probability that the mean number of calories ingested is more than 2800?

A random sample of 20 employees was collected from Brac University, to estimate the average daily time they spent on social media. Suppose that the population times have a normal distribution with a mean of 95 minutes and a standard deviation of 23 minutes. a. Find the probability that the sample mean more than 85 minutes.(answer in three decimal places)  b. What is the probability that the sample mean is outside the range of 90 to 100 minutes? (answer in three decimal places)

A health expert evaluates the sleeping patterns of adults. Each week she randomly selects 40 adults and calculates their average sleep time. Over many weeks, she finds that 5% of average sleep time is less than 3 hours and 5% of average sleep time is more than 3.4 hours. What are the mean and standard deviation (in hours) of sleep time for the population? (Round "Mean" to 1 decimal places and "standard deviation" to 3 decimal places.) Mean Standard deviation

You hope to rent an unfurnished one-bedroom apartment in Dallas next year. You call a friend who lives there and ask him to give you an estimate of the mean monthly rate. Having recently taken a statistics course, your geeky friend asks about the desired margin of error and confidence level for the estimate. He also tells you that the standard deviation of monthly rents for one-bedrooms is $360. Explain why in either case your geeky friend's sample may result in a bigger margin of error than desired. A bigger margin of error might result due to O rounding O a smaller guessed value for the population standard deviation sg O smaller confidence interval O a larger sample size

Given a sample with a mean of 57 and a standard deviation of 14, find x such that Pr(X > x) = 0.715. Round your answer to two decimal places, e.g. 22.96.

The results of a national survey showed that on average, adults sleep 6.9 hours per night. Suppose that the standard deviation is 1.2 hours. Round your answers to the nearest whole number. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours. At least Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 3.9 and 9.9 hours. At least Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours per day. At least How does this result compare to the value that you obtained using Chebyshev's theorem in part (a)?

Scenario 38-5. Researchers are interested in the height of the average person in San Francisco, California. Using a random sample of 1,000 people, they find that the average height in the sample is 68 inches. (Hint: Be sure to calculate the Refer to Scenario 38-5. If the standard deviation of heights is 3 inches, we can be 95% confident that the true mean height of the population is between standard error of the estimate.) O O O O between 67.997 inches and 68.003 inches. between 67.905 inches and 68.095 inches. between 67.905 inches and 68 inches. between 68 inches and 68.095 inches.

A population has a mean of 85.6, and a standard deviation of 9. Assume that a sampling distribution of sample means has been constructed, based on repeated samples of n = 225 from this population. What would be the value of the standard error of the mean? (round your answer to the neares tenth, if necessary).

SCENARIO 3 Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and a standard deviation of 3.0 while the second sample has a mean of 33.0 and a standard deviation of 4.0. Referring to Scenario 3. the pooled (i.e., combined) variance is ________

Suppose that you are interested in determining the average height of a person in a large city. You begin by collecting the heights of a random sample of 144 people from the city. The average height of your sample is 66 inches, while the standard deviation of the heights in your sample is 3 inches. The standard error of your estimate of the average height in the city is

In a hypothetical country called Tritonland, demand and supply of fish are determined by the following system of equations: Q Q = 3+P+v, where Q and P stand for quantity and price respectively, and that u and v are independent Uniform [0, 2]. Suppose we have i.i.d. observations (Qi, Pi)_1 from n markets in equilibrium. Answer the next few questions. = 15 P+u,

If the E(u|X) does not equal 0.   How can this assumption be relaxed if the sample size grows infinitely?

Question of the day: A machine is designed to produce insulating washers for electrical devices of average thickness of 0.025 cm. A random sample of 10 washers was found to have an average thickness of 0.024 cm with a standard deviation of 0.002 cm. Test the significance of the deviation. Value of t for 9 degrees of freedom at 5% level is 2.262?

The wildlife department has been feeding a special food to rainbow trout fingerlings in a pond. Based on a large number of observations, the distribution of trout weights is normally distributed with a mean of402.7grams and a standard deviation of12.8grams. What is the probability that the mean weight for a sample of 42 trout exceeds405.5grams? a.0.4338 b.1.0 c.0.5 d.0.0778

The mean output of a certain type of amplifier is 129 watts with a variance of 100. If 96 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 0.9 watts? Round your answer to four decimal places.

Consider a very large number of students taking a college entrance exam such as the SAT. And suppose the mean score on the mathematics section of the SAT is 570 with a standard deviation of 40.a. Find the z-score for a student who scored 600.b. A student is told that his z-score on this test is -1.5. What was his actual SAT math score?