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Please note that this question consists of five parts. Show all your work/explanation. Just giving the answer without adequate work/explanation may result in zero for the question.  A company is trying to decide between two methods for servicing customers’ equipment. The company serves samples of customers by one of the two methods in a random fashion. After 6 months, the company finds that 62 of 84 customers serviced by the first method are very satisfied with the service as compared to 76 of 92 customers served by the second method.  Give a point estimate of the difference in population proportions of very satisfied customers for the first and the second methods. The company is interested in testing if the true proportion of very satisfied customers is lower for the first method than for the second method. Set up appropriate null and alternative hypothesis to answer this research question.  Calculate the test statistic for the test you set up in part 2. Give the rejection region for this problem. Use 10% significance level. Write the final conclusion in the context of the problem.

In the context of a chi-square test for independence between two categorical variables, what is the following:  concluding that there is no relationship between the two variables when there really is ?

Suppose for the test of   Vs    the p value is 0.018. If the true population proportion is 0.45, then the probability of observing a test statistic as extreme or even more extreme than the one actually observed is 0.018. Is this statement true or false?

For each of the following, select the correct answer from the dropdown menu. If A and B are independent events, then

Please note that this question consists of six parts. You may use MINITAB to find a final answer. However you MUST show all the mathematical work to get to the final answer. Just giving the answer without adequate work/explanation may result in zero for the question.  The battery lifetime of particular type of calculator is supposed to last for 25,000 calculations on average.  A researcher suspect that these batteries are not as good as advertised. For a random sample of 16 batteries for such calculator type, the sample mean was found to be 24,680 calculations and standard deviation 482 calculations. Set up appropriate null and alternative hypotheses for testing the question posed by the researcher. Are the conditions to carry out the above stated test are satisfied? If the conditions are satisfied, explain how they were satisfied for this problem rather than simply giving a “yes” or “no” answer. Calculate the test statistic. Show your calculations. Find the rejection region for the test defined in part 1. Use 5% significance level. It is not sufficient to provide just the critical value. Clearly state the rejection region. Write the final conclusion in the context of the problem. Based on the decision you made in part 5, which error: type I or type II is possible? Explain. 

What method is appropriate for a study about the relationship between the type of school (private or public) and whether the school has the option of remote learning (yes or no)?

If one rejects the null hypothesis, then they could have made 

Is it truuuuue?

A small college town builds a new public parking garage in the downtown area. The town leadership plans to cover the structural cost via parking fees. The town consultant who advises the town leadership predicted $140 average revenue per weekday. The leadership wants to test if the consultant’s prediction underestimates the average revenue per weekday. For a random sample of 50 weekdays, daily fees collected resulted in an average of $125 and a standard deviation $15. The appropriate null and alternative hypotheses for this test are 

80 randomly selected PSU students were asked if they participated in at least one sport this summer, and 34 of them answered yes. A 90% confidence interval for PSU students who did not participate in at least one sport this summer is: