Exam 10: One-Sample Tests of Hypothesis

The average cost of tuition plus room and board at a small private liberal arts college is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What is the critical z value for this test?

The z or t value that separates the region of rejection from the region of non-rejection is called a __________________.

For a two-tailed hypothesis test, the computed test statistic is z = 2.65. What is the p-value?

A(n) ____________ hypothesis test is indicated if the alternate hypothesis states a direction.

In hypothesis testing, what is the level of significance?

What is the probability of making a Type II error if the null hypothesis is actually true?

A manufacturer claims that less than 1% of all its products do not meet the minimum government standards. A survey of 500 products revealed that 10 did not meet the standard. The p-value is ______________.

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 had a mean of 217.222 days and a standard deviation of 1.2019 days. What is the computed value of the test statistic?

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 H₀:?

A null hypothesis makes a claim about a __________.

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 had a mean of 217.222 days and a standard deviation of 1.2019 days. At the 0.025 significance level, decide if the sample data support the claim that shelf life has increased. State your decision in terms of the null hypothesis.

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, 12 nails (n = 12) were sampled. The mean of the sample is 41.5 and the standard deviation 1.784. To decide if the sample data support the claim that the mean length is 43 millimeters, state your decision in terms of the null hypothesis. Use a 0.02 level of significance.

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

A Type II error 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. To test the hypothesis at a 0.05 significance level, what is the decision rule?

For a two-tailed test with a 0.05 significance level, where is the rejection region when n is large and the population standard deviation is known?

Consider a two-tailed test with a level of confidence of 80.30%. The z-value is ________.

In hypothesis testing, the probability of a Type I error is also called the _________________.

Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. 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 p-value?

It is claimed that in a bushel of peaches, less than 10% are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the p-value?