# STAT 200: Introduction to Statistics Final Examination, Summer 2018 OL2

20 Problems. Please be sure to follow the answer sheet completely on the instructions(show work and provide explanations, I would also like the copy of the excel worksheet you use too). Please don’t put answers on this form. Thanks

1. Research has suggested that breakfast is the most important meal of the day. A nutritionist randomly selects 100 individuals and asks them: “Did you have breakfast this morning? Yes or no?”

(a) What is an appropriate method for graphing the data?

(b) Why is it appropriate?

2. A pet store owner is interested in the number of pets owned by her customers. She takes a random sample of 100 customers and asks them: “How many pets do you own?” (a) What is an appropriate method for graphing the data?

(b) Why is it appropriate?

3. Choose the best answer. Justify for full credit.

(a) The Knot.com surveyed nearly 13,000 couples, who married in 2017, and asked how much they spent on their wedding. The average amount of money spent on was \$33,391. The value \$33,391 is a:

(i) parameter

(ii) statistic

(iii) cannot be determined from information provided.

(b) A marketing agent asked people to rank the quality of a new soap on a scale from 1 (poor) to 5 (excellent). The level of this measurement is

(i) nominal

(ii) ordinal

(iii) interval

(iv) ratio

4. A school district wanted to assess the effectiveness of a new reading readiness program for 1st graders. The school district is divided into the individual first grade classrooms and 10 classrooms are randomly selected. All of the children in each of the 10 selected classrooms are assessed.

(a) What type of sampling method is being used?

5. The frequency distribution below shows the distribution of average seasonal rainfall in San Francisco, as measured in inches, for the years 1967-2017. (Show all work. Just the answer, without supporting

work, will receive no credit.)

 Season Rainfall (in Inches) Frequency Cumulative Relative Frequency 0 – 9.99 1 10 – 19.99 22 20 – 29.99 0.84 30 – 30.99 0.98 40 – 40.99 1.00 Total 50

(a) Complete the frequency table with frequency and cumulative relative frequency. Express the cumulative relative frequency to two decimal places.

(b) What percentage of season in this sample has a seasonal rainfall between 30 and 40.99 inches, inclusive?

(c) Which of the following seasonal rainfall groups does the median of this distribution belong to?

10-19.99, 20 – 29.99, or 30 – 39.99? Why?

6. Consider selecting one card at a time from a 52-card deck. What is the probability that the first card is a diamond and the second card is also a diamond? Express the probability in fraction format. (Note: There are 13 diamonds in a deck of cards) (Show all work. Just the answer, without supporting work, will receive no credit.)

(a) Assuming the card selection is without replacement.

(b) Assuming the card selection is with replacement.

7. Mimi has seven new summer outfits. She plans to pack three of the new summer outfits in her trip to Tokyo.

(a) How many different ways can the three summer outfits be selected?

(b) Please describe the method used and the reason why it is appropriate for answering the question. Just the answer, without the description and reason, will receive no credit.

8. A businessman needs to visit clients in 5 different cities.

(a) How many different routes can he take?

(b) Please describe the method used and the reason why it is appropriate for answering the question. Just the answer, without the description and reason, will receive no credit.

9. Recent research suggests that car ownership may have peaked. The following probability distribution table shows the random variable, x, where x is number of cars owned by household:

 x P(x) 0 0.10 1 0.19 2 0.45 3 0.22 4 0.04

(a) Determine the mean of (Round the answer to two decimal places). Show all work. Answers without supporting work will not receive credit.

(b) Determine the standard deviation of x. (Round the answer to two decimal places) Show all work. Answers without supporting work will not receive credit.

10. Max Scherzer, the starting pitcher for the Nationals, on average, has a 0.250 probability of hitting the ball in a single “at bat”. In one game, he gets 6 “at bats.”

(a) Let X be the number of hits that Max gets. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?

(b) Find the probability that he gets at least 4 hits in the one game. (Round the answer to 3 decimal places) Show all work. Just the answer, without supporting work, will receive no credit.

11. Assume that gas mileage for cars is normally distributed with a mean of 23.5 miles per gallon and a standard deviation of 10 miles per gallon. Show all work. Just the answer, without supporting work, will receive no credit.

(a) What is the probability that a randomly selected car gets between 20 and 25 miles per gallon? (Round the answer to 4 decimal places)

(b) Find the 80th percentile of the miles per gallon distribution. (Round the answer to 2 decimal places)

Based on the performance of all individuals who tested between July 1, 2013 and June 30, 2016, the GRE Verbal Reasoning scores are normally distributed with a mean of 149.97 and a standard deviation of 8.49. (https://www.ets.org/s/gre/pdf/gre_guide_table1a.pdf). Show all work. Just the answer, without supporting work, will receive no credit.

(c) For a sample of size 64, state the standard deviation of the sample mean (the “standard error of the mean”). (Round your answer to three decimal places)

(d) Suppose a sample of size 64 is taken. Find the probability that the sample mean GRE Verbal Reasoning scores is more than 152. (Round your answer to three decimal places)

12. The color distribution of plain M&M’s varies by the factory in which they were made. The Hackettstown, New Jersey plant uses the following color distribution for plain M&M’s: 12.5% red, 25% orange, 12.5% yellow, 12.5% green, 25% blue, and 12.5% brownEach piece of candy in a random sample of 100 plain M&M’s from the Hackettstown factory was classified according to colorand the results are listed below. Use a 0.05 significance level to test the claim that the Hackettstown factory color distribution is correct. Describe method used for calculating answer.

 Color Red Orange Yellow Green Blue Brown Number 11 28 20 9 20 12

(a) Identify the appropriate hypothesis test and explain the reasons why it is appropriate for analyzing this data.

(b) Identify the null hypothesis and the alternative hypothesis.

(c) Determine the test statistic. (Round your answer to two decimal places)

(d) Determine the p-value. (Round your answer to two decimal places)

(e) Compare p-value and significance level α. What decision should be made regarding the null hypothesis (e.g., reject or fail to reject) and why?

(f) Is there sufficient evidence to support the claim that the Hackettstown factory color distribution is correct? Justify your answer.

13. A survey showed that 680 of the 1000 adult respondents believe in global warming.

(a) Construct a 95% confidence interval estimate of the proportion of adults believing in global warming. (Round the lower bound and upper bound of the confidence interval to three decimal places) Include description of how confidence interval was constructed.

(b) Describe the results of the survey in everyday language.

14. In a study to assess the effectiveness of garlic for lowering cholesterol, 60 adults were treated with garlic tablets. Cholesterol levels were measured before and after treatment. The changes in their LDL cholesterol (in mg/dL) have a mean of 7 and a standard deviation of 4.

(a) Construct a 90% interval estimate of the mean change in LDL cholesterol after the garlic tablet treatment. (Round the lower bound and upper bound of the confidence interval to two decimal places) Include description of how confidence interval was constructed.

(b) Describe the results of the study in everyday language.

15. A health educator was interested in determining whether college students at her college really do gain weigh during their freshman year. A random sample of 5 college students was chosen and the weight for each student was recorded in August and May. Does the data below suggest that college students gain weight during their freshman year? The health educator wants to use a 0.05 significance level to test the claim.

 Weight (pounds) Student August May 1 2 3 4 5 175 170 135 160 200 180 164 142 166 208

(a) What is the appropriate hypothesis test to use for this analysis? Please identify and explain why it is appropriate.

(b) Let μ1 = mean weight in May. Let μ2 = mean weight in August. Which of the following statements correctly defines the null hypothesis?

(i) μ1 – μ2 > 0 (μd > 0)

(ii) μ1 – μ2 = 0 (μd = 0)

(iii) μ1 – μ2 < 0 (μd < 0)

(c) Let μ1 = mean weight in May. Let μ2 = mean weight in August. Which of the following statements correctly defines the alternative hypothesis?

(i) μ1 – μ2 > 0 (μd > 0)

(ii) μ1 – μ2 = 0 (μd = 0)

(iii) μ1 – μ2 < 0 (μd < 0)

(d) Determine the test statistic. Round your answer to three decimal places. Describe method used for obtaining the test statistic.

(e) Determine the p-value. Round your answer to three decimal places. Describe method used for obtaining the p-value.

(f) Compare p-value and significance level α. What decision should be made regarding the null hypothesis (e.g., reject or fail to reject) and why?

(g) What do the results of this study tell us about freshman college student weight gain? Justify your conclusion.

17. A psychologist is interested in studying the effectiveness of different therapies for depression. The psychologist selects 90 clients and randomly assigns thirty to each of the following groups:

cognitive-behavioral treatment, psychodynamic psychotherapy, or client-centered treatment. The dependent measure is a score on a depression inventory after 4 weeks of treatment. The psychologist wants to test the claim that all three therapies are equally effective in reducing symptoms of depression.

(a) Which statistical approach should be used?

i. confidence interval

ii. t-test

iii. ANOVA

iv. Chi square

(b) Explain the rationale for your selection in (a). Specifically, why would this be the appropriate statistical approach?

18. A study was conducted to see whether monetary incentives to use less water during times of drought had an effect on water usage. Sixty single family homeowners were randomly assigned to one of two groups: 1) monetary incentives and 2) no monetary incentives. At the end of three months, the total amount of water usage for each household, in gallons, was measured.

(a) What would be the appropriate hypothesis test to use to test the claim that monetary incentives reduce water usage?

i. t-test for two independent samples

ii. t-test for dependent samples

iii. z-test for population mean

iv. correlation

(b) Explain the rationale for your selection in (a). Specifically, why would this be the appropriate statistical approach?

19. A researcher claims the proportion of auto accidents that involve teenage drivers is less than 20%. ABC Insurance Company checks police records on 400 randomly selected auto accidents and notes that teenagers were at the wheel in 64 of them. Assume the company wants to use a 0.05 significance level to test the researcher’s claim.

(a) What is the appropriate hypothesis test to use for this analysis? Please identify and explain why it is appropriate.

(b) Identify the null hypothesis and the alternative hypothesis.

(c) Determine the test statistic. Round your answer to two decimal places. Describe method used for obtaining the test statistic

(d) Determine the p-value. Round your answer to three decimal places. Describe method used for obtaining the p-value

(e) Compare p-value and significance level α. What decision should be made regarding the null hypothesis (e.g., reject or fail to reject) and why?

(f) Is there sufficient evidence to support the researcher’s claim that the proportion of auto accidents that involve teenage drivers is less than 20%? Explain your conclusion.

20. A business analyst believes that December holiday sales in 2016 are a good predictor of December holiday sales in 2017. A random sample of 8 toys stores produced the following data where is the amount of December holiday sales in 2016 and is the amount of December sales in 2017, in dollars.

 x y 10257 11689 6556 6438 7224 8662 9987 9454 11568 12004 8453 8231 4235 5048 5576 4850

(a) Find an equation of the least squares regression line. Round the slope and y-intercept value to two decimal places. Describe method for obtaining results.

(b) Based on the equation from part (a), what is the predicted 2017 December holiday sales if the 2016 December holiday sales is 6,000 dollars? Show all work and justify your answer.

(c) Based on the equation from part (a), what is the predicted 2017 December holiday sales if the 2016 December holiday sales is 20,000 dollars? Show all work and justify your answer.

(d) Which predicted 2017 holiday sales that you calculated for (b) and (c) do you think is closer to the true 2017 holiday sales and why?

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