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.

A carpenter is making doors that are 2058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 751 doors is made, and it is found that they have a mean of 2047 millimeters with a standard deviation of 32. Is there evidence at the 0.1 level that the doors are too short and unusable?
State the null and alternative hypotheses for the above scenario.

A group of local businessmen is thinking about developing land into a shopping mall. To evaluate the desirability of the location, they count the number of shoppers who visit the neighboring shopping center each day. A random sample of 55 days reveals a daily average of 91 shoppers with a standard deviation of 46 shoppers. The businessmen will develop the land if the average number of shoppers per day is more than 80. Based on the sample data, should the businessmen develop the land? Perform a hypothesis test and use a significance level of α=0.01
. Assume the population of the number of daily shoppers is approximately normally distributed.
State the null and alternative hypotheses for the test. Fill in the blank below.

H0Ha: μ=80: μ ? 80
b. Compute the value of the test statistic. Round your answer to three decimal places.
c. Draw a conclusion and interpret the decision.

The mayor of a town believes that over 49% of the residents favor annexation of an adjoining bridge. Is there sufficient evidence at the 0.01 level to support the mayor's claim? After information is gathered from 320 voters and a hypothesis test is completed, the mayor decides to reject the null hypothesis at the 0.01
level.

What is the conclusion regarding the mayor's claim?