Question

Please answer both!!

Suppose the national average dollar amount for an automobile insurance claim is $805.66. You work for an agency in Michigan and you are interested in whether or not the state average is less than the national average. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≥ 805.66, Alternative Hypothesis: μ < 805.66. You take a random sample of claims and calculate a p-value of 0.02 based on the data, what is the appropriate conclusion? Conclude at the 5% level of significance.

Question 12 options:

1)	The true average claim amount is significantly higher than $805.66.

2)	The true average claim amount is higher than or equal to $805.66.

3)	The true average claim amount is significantly less than $805.66.

4)	The true average claim amount is significantly different from $805.66.

5)	We did not find enough evidence to say the true average claim amount is less than $805.66.

It is believed that students who begin studying for final exams a week before the test score differently than students who wait until the night before. Suppose you want to test the hypothesis that students who study one week before score different from students who study the night before, giving you the following hypotheses: Null Hypothesis: μ₁ = μ₂, Alternative Hypothesis: μ₁ ≠ μ₂. A random sample of 40 students who indicated they studied early shows an average score of 90.78 (SD = 4.15) and 29 randomly selected procrastinators had an average score of 88.15 (SD = 6.977). Perform a two independent samples t-test assuming that early studiers are group 1 and procrastinators are group 2. What is the test statistic and p-value of this test? Assume the population standard deviations are the same.

Question 14 options:

1)	Test Statistic: -1.957, P-Value: 0.0545

2)	Test Statistic: 1.957, P-Value: 0.0545

3)	Test Statistic: 1.957, P-Value: 1.9728

4)	Test Statistic: 1.957, P-Value: 0.9728

5)	Test Statistic: 1.957, P-Value: 0.0272

Answer 1

Solution :

12)

P-value = 0.02

P-value < 0.05

Reject the null hypothesis

The appropriate conclusion is :

The true average claim amount is significantly less than $805.66.

Option 3)

14)

Test Statistic: 1.957, P-Value: 0.0545

Option 2)