1. For each statement below, determine whether it is true or false.

a. A researcher performed the following hypothesis test: 0: = 35 : < 35 The test statistic for the test was t = 2.7069 and the p-value was 0.995. The alternative hypothesis was supposed to be : 35 which means the p-value for the test should be 1.99.

b. A 95% confidence interval for estimating is calculated to be (62.2528, 73.2156). The margin of error for this interval is 10.9628 c. For a given sample size, the t critical value corresponding to a 95% confidence interval is greater than the t critical value corresponding to a 90% confidence interval.

2. In 2020, the average national cost for health insurance was $456 per month for an individual. It is believed that the current average is higher than this. To investigate this claim, a sample of 126 individual health insurance plans is selected. The average cost of the plans in this sample is $470.23 with a standard deviation of $48.56.

a. Conduct the appropriate hypothesis test at the 0.05 level of significance. (possible p-values: 0.0007, 0.0014, 0.9993)

b. Based on the decision made in part a, what type of error is possible?

c. Describe the error you selected in part b in the context of this problem by choosing one correct option for each of the two parts shown. The data leads us to support/not support (choose 1) the claim that the mean cost of an individual health insurance plan is more than $456 per month, when in reality the mean is/is not (choose 1) more than $456 per month