4.30 Car insurance savings, Part I. A car insurance company advertises that customers switching to their insurance save, on average, $432 on their yearly premiums. A market researcher at a competing insurance discounter is interested in showing that this value is an overestimate so he can provide evidence to government regulators that the company is falsely advertising their prices. He randomly samples 82 customers who recently switched to this insurance and nds an average savings of $395, with a standard deviation of $102. Are conditions for inference satis ed? (b) Perform a hypothesis test and state your conclusion. Do you agree with the market researcher that the amount of savings advertised is an overes- timate? Explain your reasoning. (d) Calculate a 90% con dence interval for the average amount of savings of all customers who switch their insurance. e) Do your results from the hypothesis test and the con dence interval agree? Explain.
Paired or not? In each of the following scenarios, determine if the data are paired. We would like to know if Intel's stock and Southwest Airlines' stock have similar rates of return. To nd out, we take a random sample of 50 days for Intel's stock and another random sample of 50 days for Southwest's stock. (b) We randomly sample 50 items from Target stores and note the price for each. Then we visit Walmart and collect the price for each of those same 50 items. A school board would like to determine whether there is a di erence in average SAT scores for students at one high school versus another high school in the district. To check, they take a simple random sample of 100 students from each high school
5.6 Paired or not? In each of the following scenarios, determine if the data are paired. We would like to know if Intel's stock and Southwest Airlines' stock have similar rates of return. To nd out, we take a random sample of 50 days for Intel's stock and another random sample of 50 days for Southwest's stock. (b) We randomly sample 50 items from Target stores and note the price for each. Then we visit Walmart and collect the price for each of those same 50 items. (c ) A school board would like to determine whether there is a di erence in average SAT scores for students at one high school versus another high school in the district. To check, they take a simple random sample of 100 students from each high school.
5.8 Work hours and education, Part I. The General Social Survey collects data on demo- graphics, education, and work, among many other characteristics of US residents. The histograms below display the distributions of hours worked per week for two education groups: those with and without a college degree.37 Suppose we want to estimate the average di erence between the number of hours worked per week by all Americans with a college degree and those without a college degree. Summary information for each group is shown in the tables. 0 20 40 60 80
0 20 40 60 80 0 100 200 College degree Hours worked per week 0 20 40 60 800 20 40 60 80 0 125 250 No college degree College degree Mean 41.8 hrs SD 15.1 hrs n 505 No college degree Mean 39.4 hrs SD 15.1 hrs n 667 What is the parameter of interest, and what is the point estimate? (b) Are conditions satis ed for estimating this di erence using a con dence interval? Create a 95% con dence interval for the di erence in number of hours worked between the two groups, and interpret the interval in context. (d) Can you think of any real world justi cation for your results? (Note: There isn't a single correct answer to this question.)
5.24 Oscar winners. The rst Oscar awards for best actor and best actress were given out in 1929. The histograms below show the age distribution for all of the best actor and best actress winners from 1929 to 2012. Summary statistics for these distributions are also provided. Is a t test appropriate for evaluating whether the di erence in the average ages of best actors and actresses might be due to chance? Explain your reasoning.41 20 40 60 80 0 10 20 Best actress Ages (in years) 20 40 60 80 0 10 20 Best actor Best Actress Mean 35.6 SD 11.3 n 84 Best Actor Mean 44.7 SD 8.9 n 84 41Oscar winners from 1929 { 2012, data up to 2009 from the Journal of Statistics Education data archive and more current data from wikipedia.org.
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