Exam 10: One-Sample Tests of Hypothesis

Test at the 0.01 level the statement that 55% of those families who plan to purchase a vacation residence in Florida want a condominium. The null hypothesis is $\pi$ = 0.55 and the alternate is $\pi$ $\neq$ .55. A random sample of 400 families who planned to buy a vacation residence revealed that 228 families want a condominium. What decision should be made regarding the null hypothesis?

If 20 out of 50 students sampled live in a college dormitory, what is the estimated proportion of students at the University living in a dormitory?

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. To test the hypothesis at a 0.05 significance level, what is the test statistic? _______________

What do we call the statement that determines if the null hypothesis is rejected?

What value is the dividing point separating the region of rejection from the region of non-rejection? ___________________________

An example of a hypothesis is: a person is innocent until proven guilty.

For a one-tailed test using the 0.05 level of significance, the critical value for the z test is 1.645, but for t it is 1.96.

Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the null hypothesis?

A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine boxes of cake mix gave these shelf lives (in days): 215, 217, 218, 219, 216, 217, 217, 218 and 218. At the 0.025 level, has the shelf life of the cake mix increased?

What is the critical value of t for an alternative hypothesis of µ > 30, a 1% level of significance and a sample size of 8? ___________

It is claimed that in a bushel of peaches, less than ten percent are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the null hypothesis?

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean 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. What is the sample mean?

The probability of a Type II error is represented by

A machine cuts steel to length for nails. The mean length of a nail is 43 millimeters. There is concern that the settings of the machine producing the nails have changed. To test the claim, twelve nails (n = 12) were sampled. The mean of the sample is 41.5 and the standard deviation is 1.784. What is the value of the test statistic?