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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: 

Identify whether it is more appropriate to make inference on population mean or population proportion, if you study 

A company director wants to study the relationship between the company’s sales and the population size by zip code. Her assistant regressed the population size on the sales (i.e. sales as the explanatory variable and population size as the response) and obtained 42% as the coefficient of determination R2 for the model. But the director is interested in knowing the amount of variation in sales explained by the population size, i.e. the coefficient of determination for the regression line with population size as the explanatory variable and sales as the response. 

An article reports that the 95% confidence interval for the true proportion of adults in United States who are afraid to fly is (0.245, 0.297) based on a random sample of size 250. What is the point estimate of the true proportion of adults in United States who are afraid to fly? [fill1] What is the correct interpretation of this interval? [fill2]