## Statistics Assignment

1. 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?

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

(a) 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) interval (ii) nominal (iii) ordinal (iv) ratio

(b) A STAT 200 instructor surveyed nearly 100 students, who took STAT 200 in Fall 2018, and asked how many hours they spent on STAT 200 each week. The average hours spent was 12.25 hours. The value 12.25 is a: (i) parameter (ii) statistic (iii) population (iv) sample 3. 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.) STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL4 3

(a) Why is it appropriate to use a grouped frequency distribution for this data?

(b) Complete the frequency table with frequency and cumulative relative frequency. Express the cumulative relative frequency to two decimal places. (c) What percentage of season in this sample has a seasonal rainfall between 0 and 19.99 inches, inclusive?

(d) 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? 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?

(b) Please explain your answer. 5. A study was conducted to determine whether the mean braking distance of four-cylinder cars is greater than the mean braking distance of six-cylinder cars.

A random sample of 20 four-cylinder cars and a random sample of 20 six-cylinder cars were obtained, and the braking distances were measured. (a) What would be the appropriate hypothesis test for this analysis? (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? 6. A study of 10 different weight loss programs involved 500 subjects. Each of the 10 programs had 50 subjects in it. The subjects were followed for 12 months. Weight change for each subject was recorded. The researcher wants to test the claim that all ten programs are equally effective in weight loss. (a) Which statistical approach should be used? (i) confidence interval (ii) t-test (iii) ANOVA STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL4 4 (iv) Chi square (b) Explain the rationale for your selection in (a). Specifically, why would this be the appropriate statistical approach? 7. A STAT 200 professor took a sample of 10 midterm exam scores from a class of 30 students. The 10 scores are shown in the table below: (a) What is the sample mean? (b) What is the sample standard deviation? (Round your answer to two decimal places) (c) If you leveraged technology to get the answers for part (a) and/or part (b), what technology did you use? If an online applet was used, please list the URL, and describe the steps. If a calculator or Excel was used, please write out the function. 8. There are 15 members on the board of directors for a Fortune 500 company. If they must select a chairperson, a first vice chairperson, a second vice chairperson, and a secretary. (a) How many different ways the officers can 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. 9. Amy has six books from the Statistics is Fun series. She plans on bringing two of the six books with her in a road trip. (a) How many different ways can the two books 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. 10. There are 4 suits (heart, diamond, clover, and spade) in a 52-card deck, and each suit has 13 cards. Suppose your experiment is to draw one card from a deck and observe what suit it is. Express the probability in fraction format. (Show all work. Just the answer, without supporting work, will receive no credit.) STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL4 5 (a) Find the probability of drawing a heart or diamond. (b) Find the probability that the card is not a spade. 11. An airline company has a policy of routinely overbooking flights. The following probability distribution table shows the random variable, x, where x is number of passengers who cannot be boarded because there are more passengers than seats: (a) Determine the mean of x (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. 12. 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 3 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. Refer to the following information for Questions 13 and 14. STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL4 6 The heights of pecan trees are normally distributed with a mean of 10 feet and a standard deviation of 2 feet. 13. Show all work. Just the answer, without supporting work, will receive no credit. (a) What is the probability that a randomly selected pecan tree is between 9 and 12 feet tall? (Round the answer to 4 decimal places) (b) Find the 80th percentile of the pecan tree height distribution. (Round the answer to 2 decimal places) 14. Show all work. Just the answer, without supporting work, will receive no credit. (a) For a sample of 36 pecan trees, state the standard deviation of the sample mean (the “standard error of the mean”). (Round your answer to three decimal places) (b) Suppose a sample of 36 pecan trees is taken. Find the probability that the sample mean heights is between 9.5 and 10 feet. (Round your answer to four decimal places) 15. A survey showed that 980 of the 1500 adult respondents believe in global warming. (a) Construct a 99% 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. 16. In a study to assess the effectiveness of garlic for lowering cholesterol, 50 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 8 and a standard deviation of 4. (a) Construct a 95% 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. 17. An AP Statistics teacher claims that the AP Statistics grade distribution is as follows: STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL4 7 Suppose that a sample of 100 students taking AP Statistics class yields the observed counts shown below: Use a 0.10 significance level to test the claimed AP Statistics grade distribution is correct. (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 that the claimed AP Statistics grade distribution is correct? Justify your answer. 18. Mimi was curious if regular excise really helps weight loss, hence she decided to perform a hypothesis test. A random sample of 5 UMUC students was chosen. The students took a 30- minute exercise every day for 6 months. The weight was recorded for each individual before and after the exercise regimen. Does the data below suggest that the regular exercise helps weight loss? Assume Mimi wants to use a 0.05 significance level to test the claim. STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL4 8 (a) What is the appropriate hypothesis test to use for this analysis: z-test for two proportions, t-test for two proportions, t-test for two dependent samples (matched pairs), or t-test for two independent samples? Please identify and explain why it is appropriate. (b) Let μ1 = mean weight before the exercise regime. Let μ2 = mean weight after the exercise regime. 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 before the exercise regime. Let μ2 = mean weight after the exercise regime. Which of the following statements correctly defines the alternative hypothesis? (a) μ1 – μ2 > 0 (μd > 0) (b) μ1 – μ2 = 0 (μd = 0) (c) μ1 – μ2 < 0 (μd < 0) (d) Determine the test statistic. Round your answer to three decimal places. Show all work; writing the correct test statistic, without supporting work, will receive no credit. (e) Determine the p-value. Round your answer to three decimal places. Show all work; writing the correct critical value, without supporting work, will receive no credit. (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) Is there sufficient evidence to support the claim that regular exercise helps weight loss? Justify your conclusion. 19. A researcher claims that more than 75% of the adults believe in global warming. Ryan conducted a survey on a random sample of 200 adults. The survey showed that 155 adults in the sample believe in global warming. Assume Ryan 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? STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL4 9 (f) Is there sufficient evidence to support the researcher’s claim that more than 75% of the adults believe in global warming? 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 x is the amount of December holiday sales in 2016 and y is the amount of December sales in 2017, in dollars. (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 predicted 2017 holiday sales and why?

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