Stats HW. Please Show all work. Question 1 Part (a) Chicken Delight claims that the mean wait time for an order is 7 minutes or less. A sample of 50 orders revealed a mean wait time of 7.2 minutes. The standard deviation is 1 minute. Using a level of significance of 0.05, carry out a hypothesis test for Chicken Delight's claim. Part (b) Chicken Delight claims that the mean wait time for an order is 7 minutes or less. A sample of 200 orders revealed a mean wait time of 7.2 minutes. The standard deviation is 1 minute. Using a level of significance of 0.05, carry out a hypothesis test for Chicken Delight's claim. Part (c) Compare your results from Parts (a) and (b) and provide a mathematical explanation for what you find. Part (d) Compare your results from Parts (a) and (b) and provide an intuitive explanation for what you find, i.e., why does it make sense that the different sample sizes would change the outcome of the hypothesis test when the rest of the information is unchanged Question 2 Suppose that you want to test the claim that the mean thickness of an iPad screen is 2.5 millimeters. You collect a sample of 80 iPads to carry out a hypothesis test, using a significance level (alpha) of 0.05. Your decision is to not reject the null hypothesis. Part (a) Using the information above, what is the smallest possible p-value for this scenario? Part (b) Using the information above, what is the largest possible p-value for this scenario? Question 3 Part (a) The following information is given: - The null hypothesis is that the mean weight of a niffler is 3.5 ounces. The sample mean is 3.1 ounces and the sample standard deviation is 0.4 ounces. The test statistic has a standard normal distribution (if H0 is true). If it is possible to determine the critical value(s) based on this information, determine it/them. If it is not possible, explain why it is not possible. Page 1 of 2 Part (b) Part (b) is independent from Part (a), i.e., do not use information from Part (a) to answer Part (b). The following information is given: - The sample consists of 212 cars driving on I-95. Their mean speed is 64 miles per hour. The significance level is 0.01. The test statistic has a standard normal distribution (if H0 is true). If it is possible to determine the critical value(s) based on this information, determine it/them. If it is not possible, explain why it is not possible. Page 2 of 2