Exam 10: One-Sample Tests of Hypothesis

The waiting time for patients at a local walk-in health clinic follows a normal distribution with a mean of 15 minutes and a population standard deviation of 5 minutes. The quality-assurance department sampled 50 patients and found that the mean waiting time was 13.25 minutes. At the 0.025 significance level, decide if the sample data support the claim that the mean waiting time is less than 15 minutes. State your decision in terms of the null hypothesis.

A tire manufacturing company is reviewing its warranty for their rainmaker tire. The warranty is for 40,000 miles. The distribution of tire wear is normally distributed with a population standard deviation of 15,000 miles. The tire company believes that the tire actually lasts more than 40,000 miles. A sample of 49 tires revealed that the mean number of miles is 45,000 miles. Test the hypothesis with a 0.05 significance level. What is our decision?

A random sample of size 15 is selected from a normal population. The population standard deviation is unknown. Assume the null hypothesis indicates a two-tailed test and the researcher decided to use the 0.10 significance level. For what values of t will the null hypothesis not be rejected?

What are the critical z-values for a two-tailed hypothesis test if α = 0.01?

The level of significance is the probability of rejecting the null hypothesis when it is actually true.

A tire manufacturing company is reviewing its warranty for their rainmaker tire. The warranty is for 40,000 miles. The distribution of tire wear is normally distributed with a population standard deviation of 15,000 miles. The tire company believes that the tire actually lasts more than 40,000 miles. A sample of 49 tires revealed that the mean number of miles is 45,000 miles. What is H₁:?

One of the major U.S. tire makers wishes to review its warranty for their rainmaker tire. The warranty is for 40,000 miles. The distribution of tire wear is normally distributed with a population standard deviation of 15,000 miles. The tire company believes that the tire actually lasts more than 40,000 miles. A sample of 49 tires revealed that the mean number of miles is 45,000 miles. If we test the hypothesis with a 0.05 significance level, what is the probability of a Type II error if the actual tire mileage is 42,000 miles?

The mean weight of newborn infants at a community hospital is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. Does the sample data show a significant increase in the average birthrate at a 5% level of significance?

The Greek letter _________ is used to represent the probability of making a Type I error.

Define the level of significance.