Final Exam for Statistics

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Strayer University *

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135

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Statistics

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Jan 9, 2024

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20/25 that's 80% RETAKE 20 questions were answered correctly . 5 questions were answered incorrectly . 1 Sara wonders what percentage of her students answered at least half of the quiz questions incorrectly. The relative cumulative frequency of students who earned a score of 20 or lower on the quiz is __________ .  34%  14%  28%  68% RATIONALE To get the relative frequency of 20 or lower, we need to find the cumulative number of 20 or less. We simply add up any bin that has the number 20 or less, such as the bin that shows scores of 1-5, 6-10, 11-15, and 16-20. This would be: To get relative frequency, we will take this cumulative number and divide it by the total number of students.

CONCEPT Cumulative Frequency 2 The average number of road accidents that occur on a particular stretch of road during a month is 7. What is the probability of observing exactly three accidents on this stretch of road next month?  0.048  0.023  0.020  0.052 RATIONALE Since we are finding the probability of a given number of events happening in a fixed interval when the events occur independently and the average rate of occurrence is known, we can use the following Poisson distribution formula: The variable k is the given number of occurrences, which in this case, is 3 accidents. The variable λ is the average rate of event occurrences, which in this case, is 7 accidents. CONCEPT Poisson Distribution 3 A survey asked 1,000 people which magazine they preferred, given three choices. The table below breaks the votes down by magazine and age group.

Age Below 40 Age 40 and The National Journal 104 200 Newsday 120 230 The Month 240 106 If a survey is selected at random, what is the probability that the person voted for "Newsday" and is also age 40 or older? Answer choices are rounded to the hundredths place.  0.54  0.66  0.23  0.34 RATIONALE If we want the probability of people who voted for "Newsday" and are also age 40 and over, we just need to look at the box that is associated with both categories, or 230. To calculate the probability, we can use the following formula: CONCEPT Two-Way Tables/Contingency Tables 4 The weekly salaries of full-time and part-time employees at a company are listed on the table. What does the circled section represent?  Sixty-eight full-time employees earn $34 per week.

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 Two part-time employees earn between $680 and $690 per week.  Two full-time employees earn more than $680 per week.  Thirty-four part-time employees earn more than $680 per week. RATIONALE If we recall that the stem and leaf can give us the actual values in the data set, then the circle corresponds to $683 and $684. We can then note that there are two part-time workers who make between $680 and $690. CONCEPT Stem-and-Leaf Plots 5 The owner of a new store on Main Street wants to turn the boulevard outside into extra parking spaces because she is concerned about parking availability. She randomly selects 500 residents of the town to take a survey, and these individuals have confirmed their participation. One of the survey questions reads, “Many residents believe the lack of available parking on Main Street is a major problem, and extra spaces along the boulevard would help. Do you agree?" The store owner's survey could suffer from which type of bias?  There is no evidence of bias in the way this survey is carried out.  Selection bias  Response bias  Nonresponse bias RATIONALE

By stating that many residents already believe parking is an issue and putting a response inside of the question, this is a good example of response bias. CONCEPT Nonresponse and Response Bias 6 The blood bank at a hospital has 1,200 units of blood, out of which 37% units are of blood group B+. A clinical researcher randomly selects 300 units of blood and finds that 33% of those are of blood group B+. To test his result, he randomly selects 200 units of blood and finds that 40% of those are of blood group B+. Which of the following is the reason there is a difference between the two percentages selected by the researcher?  Both samples suffered from non-response bias.  The samples were not random samples.  The sample sizes were both too small.  Random error; the numbers were different due to variability inherent in sampling. RATIONALE When sampling, there is always some variability that occurs. So, although the sample values are different, since they were randomly chosen, the differences are simply due to the variability that comes from sampling and not due to some systematic bias. CONCEPT Random and Systematic Errors 7 For a set of data, x is the explanatory variable. Its mean is 8.2, and its standard deviation is 1.92. For the same set of data, y is the response variable. Its mean is 13.8, and its standard deviation is 3.03.

The correlation was found to be 0.223. Select the correct slope and y-intercept for the least-squares line. Answer choices are rounded to the hundredths place.  Slope = 0.14 y-intercept = 12.65  Slope = 0.35 y-intercept = 3.37  Slope = 0.35 y-intercept = 10.93  Slope = 0.14 y-intercept = 6.27 RATIONALE We first want to get the slope. We can use the formula: To then get the intercept, we can solve for the y-intercept by using the following formula: We know the slope, , and we can use the mean of x and the mean of y for the variables and to solve for the y-intercept, . CONCEPT

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Finding the Least-Squares Line 8 A university wants to survey its undergraduates about their satisfaction with the new website. The university researchers pasted a link to the survey on the new website. A majority of the surveys showed that students were happy with the new website and found it easy to use. The university concluded that the website was fine and did not make any changes. However, on Friday, hundreds of students turned up at the Undergraduate Student Committee meeting complaining about how difficult it was to navigate the new website. University researchers realized that placing the survey on the website meant that people who liked the website were more likely to access the survey. Which of the following types of bias affected the survey's conclusions?  Deliberate bias  Selection bias  Response bias  Non-response bias RATIONALE Selection bias is when the mode of selection introduces a bias in the sample so that it is not representative of the population of interest. Since they only collected information from those who used the website, this does not represent how students in general feel about the website and is therefore an example of selection bias. CONCEPT Selection and Deliberate Bias 9

The first quartile (Q1) value from the above box plot is __________.  65  40  47  54 RATIONALE Note the value for Q1 is the left edge of the box, which is 47. CONCEPT Five Number Summary and Boxplots 10 Select the statement that is FALSE.  The range is never greater than the greatest value of a data set.  The interquartile range is always equal to or smaller than the range.  The mean is never greater than the greatest value of a data set.  The range is the difference between the largest and smallest values of a data set. RATIONALE If we recall, the range is the maximum value minus the minimum value. Suppose in a given dataset, the maximum value is 20 and the minimum value is -5. Then the range is equal to:

The range of 25 is larger than the maximum value of 20, so the range can certainly be larger than the max value. CONCEPT Range and Interquartile Range (IQR) 11 For the data plotted in the scatterplot, the r 2 value was calculated to be 0.9846. Which of the following sets of statements is true?  98.5% of the variation in yearly income is explained by a linear relationship with age. The correlation coefficient, r, is 0.992  98.5% of the variation in yearly income is explained by a nonlinear relationship with age. The correlation coefficient, r, is 0.992.  98.5% of the variation in age is explained by a linear relationship with yearly income. The correlation coefficient, r, is 0.969.  98.5% of the variation in age is explained by a nonlinear relationship with yearly income. The correlation coefficient, r, is 0.969. RATIONALE

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The coefficient of determination measures the percent of variation in the outcome, y, explained by the regression. So a value of 0.9846 tells us the regression with age, x, can explain about 98.5% of the variation in income, y. We can also note that r = . CONCEPT Coefficient of Determination/r^2 12 Keith tabulated the values for the average speeds on each day of his road trip as 61.5, 62.2, 55.7, 50.6, 71.3, 70.8, and 66.8 mph. He wishes to construct a 90% confidence interval. What value of t* should Keith use to construct the confidence interval? Answer choices are rounded to the thousandths place.  1.415  1.440  1.895  1.943 RATIONALE Recall that we have n = 7, so the df = n-1 = 6. So if we go to the row where df = 6 and then 0.05 for the tail probability, this gives us a value of 1.943. Recall that a 90% confidence interval would have 10% for the tails, so 5% for each tail. We can also use the last row and find the corresponding confidence level. CONCEPT How to Find a Critical T Value 13 Of 400 randomly selected people in the city of Lyon, France, 60 people had the first name Hugo.

Which of these does NOT represent inferential statistics?  15% of the people who live in Europe have the first name Hugo.  15% of the people who live in Lyon have the first name Hugo.  15% of the people who live in France have the first name Hugo.  15% of the people surveyed have the first name Hugo. RATIONALE For an inference, we use the sample information at hand to make a larger statement. Saying 15% of the people surveyed have a name of Hugo doesn't make a statement about a larger group, so it is not an inference. CONCEPT Statistics Overview 14 Using the Venn Diagram below, what is the conditional probability of event B occurring, assuming event A has happened [P(B| A)]?  0.41  0.63  0.77  0.24 RATIONALE

To get the probability of B given A has occurred, we can use the following conditional formula: The probability of A and B is the intersection, or overlap, of the Venn diagram, which is 0.41. The probability of A is all of Circle A, or 0.24 + 0.41 = 0.65. CONCEPT Conditional Probability 15 Which of the following is a condition of binomial probability distributions?  All observations are mutually exclusive.  All observations made are dependent on each other.  All observations are made randomly.  All observations made are independent of each other. RATIONALE In the binomial distribution we always assume independence of trials. This is why we simply multiply the probability of successes and failures directly to find the overall probability. CONCEPT Binomial Distribution 16 Carl recorded the number of customers who visited his new store during the week: Day Customers Monday 17

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Tuesday 13 Wednesday 14 Thursday 16 He expected to have 15 customers each day. To answer whether the number of customers follows a uniform distribution, a chi-square test for goodness of fit should be performed. (alpha = 0.10) What is the chi-squared test statistic? Answers are rounded to the nearest hundredth.  2.33  1.60  0.67  0.40 RATIONALE Using the chi-square formula we can note the test statistic is CONCEPT Chi-Square Test for Goodness-of-Fit 17 A retail brand plans to open its stores across all cities with a population of more than one million. To prepare for this, it refers to the past year's census done by the government. Which statement accurately describes the type of data the retail brand is using? 

The retail brand is relying on raw data because it has to ask for permission to use the census.  The census is an example of available data because the government provides it.  The census is an example of raw data because the government provides it.  The retail brand is relying on available data because customers provide information to the census. RATIONALE Since the retailer doesn't gather the data itself, but relies upon data that has already been collected, this is an example of using available data. CONCEPT Data 18 This scatterplot shows the maintenance expense for a truck based on its years of service. The equation for least regression line to this data set is ŷ = 76.82x + 88.56. What is the predicted value (in dollars) for maintenance expenses when a truck is 7 years old?  $549  $473  $626

 $703 RATIONALE In order to get the predicted maintenance expense when the age of the truck is 7 years, we simply substitute the value 7 in our equation for x. So we can note that: CONCEPT Predictions from Best-Fit Lines 19 A survey result shows that cell phone usage among teenagers rose from 63% in 2006 to 71% in 2008. Of the following choices, which statement about cell phone use among teenagers is true?  Cell phone usage rose by 11.2 percentage points.  Cell phone usage rose by 12.7%.  Cell phone usage rose by 12.7 percentage points.  Cell phone usage rose by 8%. RATIONALE We can note that the absolute difference between 2006 and 2008 is 63% to 71% or 8 percentage points. To get the percent difference we take the absolute difference and divide by the initial value: So we can say cell phone usage rose by 12.7%. CONCEPT

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Using Percentages in Statistics 20 Which of the following is an example of a statistic?  A local newspaper reporter asks 50 citizens for their opinion on a recent city ordinance.  Fifty households randomly sampled in one county have a mean weekly amount spent on groceries.  All 25 students in a third grade class are asked to rank their favorite fruits.  Fifty employees in a small business are randomly selected to take a survey. RATIONALE A sample is a subset of the entire group of interest. A statistic is something that comes from a sample. Since these 50 households are only a subset of all in the population, this is an example of a statistic from a sample. CONCEPT Sample Statistics and Population Parameters 21 Kate was trying to decide which type of frozen pizza to restock based on popularity: pepperoni pizza or sausage pizza. After studying the data, she noticed that pepperoni flavors sold best on the weekdays and on the weekends, but not best overall. Which paradox has Kate encountered?  Benford's Law  False Positive

 False Negative  Simpson's Paradox RATIONALE This is an example of Simpson's paradox, which is when the trend overall is not the same that is examined in smaller groups. Since the sale of pepperoni flavors on weekend/weekdays is larger but this trend changes when looking at overall sales, this is a reversal of the trend. CONCEPT Paradoxes 22 A superintendent of a school district conducted a survey to find out the level of job satisfaction among teachers. Out of 53 teachers who replied to the survey, 13 claim they are satisfied with their job. The superintendent wishes to construct a significance test for her data. She finds that the proportion of satisfied teachers nationally is 18.4%. What is the z-statistic for this data? Answer choices are rounded to the hundredths place.  1.15  0.61  2.90  1.24 RATIONALE

To make things a little easier, let's first note the denominator We can now note that Finally, subbing all in we find CONCEPT Z-Test for Population Proportions 23 Edwin conducted a survey to find the percentage of people in an area who smoked regularly. He defined the label “smoking regularly” for males smoking 30 or more cigarettes in a day and for females smoking 20 or more. Out of 635 persons who took part in the survey, 71 are labeled as people who smoke regularly. What is the 90% confidence interval for this population proportion? Answer choices are rounded to the hundredths place.  0.11 to 0.13  0.11 to 0.80  0.09 to 0.80  0.09 to 0.13 RATIONALE In order to get the CI we want to use the following form. First, we must determine the corresponding z*score for 90% Confidence Interval. Remember, this means that we have 5% for the tails, meaning 5%, or 0.05, for each tail. Using a z-table, we can find the upper z-score by finding (1 - 0.05) or 0.95 in the table. This corresponding z-score is at 1.645. We can know

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So putting it together: The lower bound is: 0.11-0.02 = 0.09 The upper bound is: 0.11 + 0.02 = 0.13 CONCEPT Confidence Interval for Population Proportion 24 Thomas was interested in learning more about the salary of a teacher. He believed as a teacher increases in age, the annual earnings also increases. The age (in years) is plotted against the earnings (in dollars) as shown below. Using the best-fit line, approximately how much money would a 45- year-old teacher make?  $58,000  $48,000  $55,000  $50,000 RATIONALE To get a rough estimate of the salary of a 45 year-old, we go to the value of 45 on the horizontal axis and then see where it falls on the best-fit line. This looks to be about $50,000. CONCEPT Best-Fit Line and Regression Line 25

When a survey was conducted among 100 students to find their favorite pizza topping, 45 students voted for pepperoni, 25 for mushrooms, and 30 voted for cheese. If a pie chart were made showing the number of votes for each topping, the central angle for the cheese sector would be __________.  90°  108°  162°  198° RATIONALE Recall that to get the angle for something in a pie chart we use the following formula: So in this case, the central angle for the cheese sector would be: CONCEPT Bar Graphs and Pie Charts

Final Exam for Statistics

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