An auto dealer would like to determine if there is a difference in the braking distance (the number of feet required to go from 60mph to 0mph) of two different models of a high-end sedan. Six drivers are randomly selected and asked to drive both models and brake once they have reached exactly 60mph. The distance required to come to a complete halt is then measured in feet. The results of the test are as follows. Can the auto dealer conclude that there is a significant difference in the braking distances of the two models? Use α=0.01. Let the braking distances of Model A represent Population 1 and the braking distances of Model B represent Population 2.
Braking Distance of High-End Sedans (Feet)
Driver 1 2 3 4 5 6
Model A 156 149 148 151 150 154
Model B 158 153 149 152 150 155
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. Make the decision and state the conclusion in terms of the original question.
d.

An SAT prep course claims to improve the test score of students. The table below shows the scores for seven students the first two times they took the verbal SAT. Before taking the SAT for the second time, each student took a course to try to improve his or her verbal SAT scores. Do these results support the claim that the SAT prep course improves the students' verbal SAT scores?
Let d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course)
. Use a significance level of α=0.05 for the test. Assume that the verbal SAT scores are normally distributed for the population of students both before and after taking the SAT prep course.
Student Score on first SAT Score on second SAT
1 380 420
2 440 530
3 470 530
4 490 550
5 440 460
6 420 490
7 410 430

a. State the null and alternative hypotheses for the test.
b. Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.
c. Compute the value of the test statistic. Round your answer to three decimal places.
d. Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.
e. Make the decision for the hypothesis test.

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.