A standardized test is given to a sixth grade class. Historically the mean score has been 173 with a variance of 30. The superintendent believes that the variance of performance may have recently increased. She randomly sampled 22 students and found a mean of 163 with a standard deviation of 5.9018. Is there evidence that the standard deviation has increased at the α=0.01 level?
State the hypotheses in terms of the standard deviation. Round the standard deviation to four decimal places when necessary.
b. Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.
c. Determine the value of the test statistic. Round your answer to three decimal places.
d. Make the decision.
e. What is the conclusion?

A national online business magazine reports that the average cost of a speeding ticket in Miami, including court fees, is $220. A local police department claims that this amount has increased. To test their claim, they collect data from a simple random sample of 16 drivers who have been fined for speeding in the last year. Assuming that the distribution of speeding ticket costs is normally distributed and the population standard deviation is $15, is there sufficient evidence to support the police department’s claim at the 0.02 level of significance?
Speeding Ticket Costs in Miami
$226 $227 $209 $231 $227 $235 $235 $216
$213 $216 $240 $235 $227 $212 $235 $236

State the null and alternative hypotheses for the test. Fill in the blank below.

H0Ha: μ=220: μblank220
b. Compute the value of the test statistic. Round your answer to two decimal places.
c. Draw a conclusion and interpret the decision.

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.

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 57 days reveals a daily average of 111 shoppers with a standard deviation of 47 shoppers. The businessmen will develop the land if the average number of shoppers per day is more than 100. 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.

a. State the null and alternative hypotheses for the test. Fill in the blank below.
H0Ha: μ=100: μblank100
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.