Insurance Company A claims that its customers pay less, on average, than customers of its competitor, Company B. You wonder if this is true, so you decide to compare the average monthly costs of similar insurance policies from the two companies. For a random sample of 20 people who buy insurance from Company A, the mean cost is $178 per month with a standard deviation of $9. For 25 randomly selected customers of Company B, you find that they pay a mean of $185 per month with a standard deviation of $12
. Assume that the population distributions are approximately normal and the population variances are not equal.

Find the P
-value for the hypothesis test. Round your answer to four decimal places.

Major television networks conducted a joint poll of viewers and asked them if they felt that beer and other alcoholic beverage commercials targeted teenagers and young adults (those under 21 years old). The results of the survey are as follows. Based on the data, can the networks conclude that the percentage of viewers who believe beer and alcoholic beverage commercials target teenagers and young adults is significantly higher in the over 30 age group than in the 30 or younger age group at α=0.01? Let the 30 or younger age group be Population 1 and let the older than 30 age group be Population 2.

Network Advertising Survey
Age Group Number Surveyed Number of "Yes" Responses
30 or Younger 1000 484
Older than 30 1000 526

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 two decimal places.
c. Make the decision and state the conclusion in terms of the original question.
d.

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.

A hospital director believes that above 77% of the test tubes contain errors and feels an audit is required. A sample of 200 tubes found 160 errors. Is there sufficient evidence at the 0.01 level to substantiate the hospital director's claim?
State the null and alternative hypotheses for the above scenario.

An independent group of food service personnel conducted a survey on tipping practices in a large metropolitan area. They collected information on the percentage of the bill left as a tip for 40 randomly selected bills. The average tip was 12.1% of the bill with a standard deviation of 2.6%. Assume that the tips are approximately normally distributed. Construct an interval to estimate the true average tip (as a percent of the bill) with 90% confidence. Round the endpoints to two decimal places, if necessary.