The admitting office at Sisters of Mercy Hospital wants to be able to inform patients of the average level of expenses they can expect per day. Historically, the average has been approximately $1190. The office would like to know if there is evidence of a decrease in the average daily billing. Seventy-five randomly selected patients have an average daily charge of $1112 with a standard deviation of $257. Conduct a hypothesis test to determine whether there is evidence that average daily charges have decreased at a significance level of α=0.02
. Assume the population of daily hospital charges is approximately normally distributed.
State the null and alternative hypotheses for the test. Fill in the blank below.

H0Ha: μ=1190: μblank1190
b. Compute the value of the test statistic. Round your answer to three decimal places.
c. Draw a conclusion and interpret the decision.

The Dodge Reports are used by many companies in the construction field to estimate the time required to complete various jobs. The company managers want to know if the time required to install 130 square feet of bathroom tile is different from the nine hours reported in the current manual. A researcher for Dodge randomly selects 54 construction workers and determines the time required to install 130 square feet of bath tile. The average time required to install the tile for the sample is 8.1 hours with a standard deviation of 3.8 hours. Use a hypothesis test to determine whether the managers’ assumptions are substantiated by the data. Use a significance level of α=0.01
. Assume the population of tile installation times is approximately normally distributed.
State the null and alternative hypotheses for the test. Fill in the blank below.

H0Ha: μ=9: μblank9
b. Compute the value of the test statistic. Round your answer to three decimal places.
c. Draw a conclusion and interpret the decision.

High-powered experimental engines are being developed by the Hendrix Motor Company for use in their new sports coupe. The engineers have calculated the maximum horsepower for the engines to be 570HP. Sixteen engines are randomly selected for testing. Perform a hypothesis test to determine whether the data suggests that the average maximum horsepower for the experimental engine is significantly different than the maximum horsepower calculated by the engineers. Assume the data are normally distributed and use a significance level of 0.05.

Maximum Horsepower (HP)
557 595 522 600 577 546 580 601
611 609 598 611 618 594 598 614

a. State the null and alternative hypotheses for the test. Fill in the blank below.
b. Compute the value of the test statistic. Round your answer to three decimal places.
c. Draw a conclusion and interpret the decision.

The Dodge Reports are used by many companies in the construction field to estimate the time required to complete various jobs. The company managers want to know if the time required to install 130 square feet of bathroom tile is different from the eight hours reported in the current manual. A researcher for Dodge randomly selects 58 construction workers and determines the time required to install 130 square feet of bath tile. The average time required to install the tile for the sample is 6.6 hours with a standard deviation of 4.1 hours. Use a hypothesis test to determine whether the managers’ assumptions are substantiated by the data. Use a significance level of α=0.02
. Assume the population of tile installation times is approximately normally distributed.
State the null and alternative hypotheses for the test. Fill in the blank below.

H0Ha: μ=8: μ ? 8
b. Compute the value of the test statistic. Round your answer to three decimal places.
c. Draw a conclusion and interpret the decision.

Determine the critical values for the confidence interval for the population standard deviation from the given values. Round your answers to three decimal places.
n=3 and α=0.2.