II. Problem Solving

1. A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 days. The standard deviation of the population is known to be 5.6 days.

1. State the null and alternative hypotheses. (6 points)

2. Compute the test statistic. (9 points)

3. What is the critical value? Using the critical value approach, test to determine if their advertisement is legitimate. Let = .05. (6 points)

2. A random sample of 49 children with working mothers showed that they were absent from school an average of 6 days per term with a standard deviation of 1.8 days.

1. Write down the equation you should use to construct the confidence interval for the average number of days absent per term for all the children. (6 points)

2. Determine a 98% confidence interval estimate for the average number of days absent per term for all the children. (8 points)

3. Determine a 95% confidence interval estimate for the average number of days absent per term for all the children. (8 points)

4. Discuss why 98% and 95% confidence intervals are different. (6 points)

3. Automobiles manufactured by the Efficiency Company have been averaging 42 miles per gallon of gasoline in highway driving. It is believed that its new automobiles average more than 42 miles per gallon. An independent testing service road-tested 36 of the automobiles. The sample showed an average of 42.8 miles per gallon with a standard deviation of 1.2 miles per gallon. With a 0.05 level of significance using the p-value approach, test to determine whether or not the new automobiles actually do average more than 42 miles per gallon.

1. State the null and alternative hypotheses. (6 points)

2. Compute the test statistic. (9 points)

3. What is the p- value associated with the sample results? What is your conclusion based on the p-value? (6 points)