Question

Suppose the national average dollar amount for an automobile insurance claim is $788.5. You work for an agency in Michigan and you are interested in whether or not the state average is greater than the national average. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≤ 788.5, Alternative Hypothesis: μ > 788.5. You take a random sample of claims and calculate a p-value of 0.0851 based on the data, what is the appropriate conclusion? Conclude at the 5% level of significance.

	1) We did not find enough evidence to say a significant difference exists between the true average claim amount and $788.5.
	2) The true average claim amount is less than or equal to $788.5.
	3) We did not find enough evidence to say the true average claim amount is higher than $788.5.
	4) We did not find enough evidence to say the true average claim amount is less than $788.5.
	5) The true average claim amount is significantly higher than $788.5.

Suppose you work for a political pollster during an election year. You are tasked with determining the projected winner of the November election. That is, you wish to determine if the number of votes for Candidate 1 is different from the votes for Candidate 2. What are the hypotheses for this test?

	1) HO: μ1 = μ2 HA: μ1 ≠ μ2
	2) HO: μ1 ≠ μ2 HA: μ1 = μ2
	3) HO: μ1 > μ2 HA: μ1 ≤ μ2
	4) HO: μ1 ≤ μ2 HA: μ1 > μ2
	5) HO: μ1 ≥ μ2 HA: μ1 < μ2

Do sit down restaurant franchises and fast food franchises differ significantly in stock price? Specifically, is the average stock price for sit-down restaurants different from the average stock price for fast food restaurants? If sit down restaurants are in group 1 and fast food restaurants are in group 2, the hypotheses for this scenario are as follows: Null Hypothesis: μ₁ = μ₂, Alternative Hypothesis: μ₁ ≠ μ₂. In a random sample of 34 sit down restaurants, you find that the average stock price is $159.45 with a standard deviation of $12.2574. For 60 fast food restaurants, the average stock price is $153.218 with a standard deviation of $9.457. Conduct a two independent sample t-test. What is the test statistic and p-value for this test? Assume the population standard deviations are the same.

	1) Test Statistic: 2.753, P-Value: 0.9964
	2) Test Statistic: 2.753, P-Value: 0.0036
	3) Test Statistic: 2.753, P-Value: 0.0071
	4) Test Statistic: 2.753, P-Value: 1.9964
	5) Test Statistic: -2.753, P-Value: 0.0071

Answer 1

Question -1

since p-value >0.05 , fail to reject H0 i.e fail to reject the claim

3)we did not find enough evidence to aay the average claim amount is higher than $788.5

Question -2) option 1

option -1 is showing correct pair of bill & alternative hypothesis

Question-3) technology output is attached below

3) test statistics: 2.753, pvalue : 0.0071