1) Late payment of medical claims can add to the cost of health care. Suppose 72.6​% of the claims were paid in full when first submitted for one insurance company. The insurance company developed a new payment system in an effort to increase this percentage. A sample of 270 claims processed under this system revealed that 202 of the claims were paid in full when first submitted. Complete parts a and b below.Based on the sample​ data, test the null hypothesis using an alpha level equal to 0.01. Discuss the results of the test.Find the​ z-test statistic.

Determine a conclusion. Choose the correct answer below.

A.Do not reject H0​, because the​ p-value is not less than the level of significance.​ Therefore, the statement that the population proportion exceeds 0.726 is not statistically supported by these sample data.

B.Reject H0​, because the​ p-value is not less than the level of significance.​ Therefore, the statement that the population proportion exceeds 0.726 is not statistically supported by these sample data.

C.Do not reject H0​, because the​ p-value is not less than the level of significance.​ Therefore, the statement that the population proportion exceeds 0.726 is statistically supported by these sample data.

D.Reject H0​, because the​ p-value is not less than the level of significance.​ Therefore, the statement that the population proportion exceeds 0.726 is statistically supported by these sample data.

2)One of the editors of a major automobile publication has collected data on 30 of the​ best-selling cars in the United States. The data are shown in the accompanying table. The editor is particularly interested in the relationship between highway mileage​ (miles per​ gallon) and curb weight of the vehicles. Complete parts a through c below. Use a significance level of 0.05 where needed.

Discuss what the plot implies about the relationship between the two variables. Choose the correct answer below.A.A​ positive, linear relationship exists between x and y.B.A​ negative, linear relationship exists between x and y.C.A​ positive, curvilinear relationship exists between x and y.D.There is no relationship.

Compute the correlation coefficient for the two variables and test to determine whether there is a linear relationship between the curb weight and the highway mileage of automobiles. r= ? ​(Round to three decimal places as​ needed.)What are the appropriate hypotheses to test for a linear​ relationship?

Calculate the​ t-test statistic for correlation.

Determine the critical​ value(s) for the rejection region for the test statistic t. Select the correct choice below and fill in the answer box to complete your choice. Assume a significance level of 0.05 for the hypothesis test.

Since the test statistic ▼ isis not in the rejection​ region, ▼ do not rejectreject the null hypothesis. Conclude there ▼ is notis a significant linear relationship between the curb weight and the highway mileage of automobiles.

Compute the linear regression equation based on the sample data. 

A car weighs approximately 4,020 pounds. Provide an estimate of the average highway mileage expected to obtain from this model.The expected highway mileage is  

3)Suppose a random sample of 80 companies taken in 2005 showed that 20 offered​ high-deductible health insurance plans to their workers. A separate random sample of 100 firms taken in 2006 showed that 44 offered​ high-deductible health insurance plans to their workers. Based on the sample​ results, can you conclude that there is a higher proportion of companies offering​ high-deductible health insurance plans to their workers in 2006 than in 2005​? Conduct your hypothesis test at a level of significance α=0.10.

Let p1 be the population proportion from 2006​, and let p2 be the population proportion from 2005. Identify the null and alternative hypotheses. Choose the correct answer below.

H0​: p1−p2=0HA​: p1−p2≠0

B.H0​: p1−p2≠0HA​: p1−p2=0

C.H0​: p1−p2≤0HA​: p1−p2>0

D.H0​: p1−p2>0HA​: p1−p2≤0

E.H0​: p1−p2<0HA​: p1−p2≥0

Calculate the test statistic.

Find the​ p-value.

State the conclusion. Choose the correct answer below.

A.Reject the null hypothesis. There is not sufficient evidence at significance level α=0.05 that the mean​ past-due amount for customers who have been called is greater than ​$40.00.

B.Do not reject the null hypothesis. There is sufficient evidence at significance level α=0.05 that the mean​ past-due amount for customers who have been called is greater than ​$40.00.

C.Do not reject the null hypothesis. There is not sufficient evidence at significance level α=0.05 that the mean​ past-due amount for customers who have been called is not equal to ​$40.00.

D.Reject the null hypothesis. There is sufficient evidence at significance level α=0.05 that the mean​ past-due amount for customers who have been called is greater than ​$40.00.