Final_Prep_Assignment (2)

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5150

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Economics

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Jan 9, 2024

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Final Prep Assignment 1. A random sample of 50 12th-grade students was asked how long it took to get to school. The sample mean was 16.2 minutes, and the sample standard deviation was 12.3 minutes. i) Find a 95% confidence interval for the population mean time it takes 12th-grade students to get to school. ii) Would a 90% confidence interval based on this sample data be wider or narrower than the 95% confidence interval? Explain. Check your answer by constructing a 90% confidence inter- val and comparing this width of the interval with the width of the 95% confidence interval you found in part i. Your stomach thinks all potatoes are mashed. 2. According to Deadline.com, the average price for a movie ticket in 2018 was $ 8.97. A random sample of movie prices in the San Francisco Bay Area 25 movie ticket prices had a sample mean of $ 12.27 with a standard deviation of $ 3.36. i) Do we have evidence that the price of a movie ticket in the San Francisco Bay Area is different from the national average? Use a significance level of 0.05. ii) Construct a 95% confidence interval for the price of a movie ticket in the San Francisco Bay Area. How does your confidence interval support your conclusion in part i? 3. In a statistics class taught by one of the authors, students took their pulses before and after being frightened. The frightening event was having the teacher scream and run from one side of the room to the other. The pulse rates (beats per minute) of the women before and after the scream were obtained separately and are shown in the table. Treat this as though it were a random sample of female community college students. Report and analyze the 98 % Confidence Interval and test the hypothesis that the mean of college women’s pulse rates is higher after a fright, using a significance level of 0.05. Make sure to state the hypothesis appropriately, and analyze your conclusion. (Relevant output on the next page) Salt is the only rock that is socially acceptable to eat 1

4. Do good smells bring good business? Previously, you examined the effects of scents on cus- tomer behavior in a small restaurant. Does a lemon odor influence the length of time customers stay in the restaurant? Report 95% confidence interval, then analyze hypothesis test at a 0.05 significance level. Compare the two and report your conclusions. 5. A 2016 Pew Research poll found that 610 out of 1000 randomly sampled U.S. adults believe that organic produce is better for health than conventionally grown varieties. i) Check the conditions for CLT. ii) Find and interpret a 95% confidence interval for the proportion of U.S. adults to believe organic produce is better for health. 6. A proponent of a new proposition on a ballot wants to know the population percentage of people who support the bill. Suppose a poll is taken, and 580 out of 1000 randomly selected people support the proposition. Should the proponent use a hypothesis test or a confidence 2

interval to answer this question? Explain. If it is a hypothesis test, state the hypotheses and find the test statistic, p-value, and conclusion. Use a 5% significance level. If a confidence interval is appropriate, find the approximate 95% confidence interval. In both cases, assume that the necessary conditions have been met. 7. Samuel Morse determined that the percentage of t’s in the English language in the 1800s was 9%. A random sample of 600 letters from a current newspaper contained 48 t’s. Using the 0.10 level of significance, test the hypothesis that the proportion of t’s in this modern newspaper is 0.09. 8. A 2018 Gallup poll asked responents if they supported same-sex marriage. Results are reported by political party in the StatCrunch output that follows. i) Test the hypothesis that support of same-sex marriage and political party affiliation are in- dependent using a significance level of 0.05. ii) Does this suggest that political parties differ significantly in their support of same-sex mar- riage? 3

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