Exam 10: One-Sample Tests of Hypothesis

The Greek letter used to represent the probability of a Type I error is alpha (α).

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

Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a mean of 22,100 miles. The fleet owner purchased 18 sets and found that the sample average life was 23,400 miles; the sample standard deviation was 1,412 miles. To determine if the spark plugs average 22,100 miles, what is the critical value for the test using a 0.05 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 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 is 1.784. To test the claim at the 0.02 significance level, what is the critical 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 z-test statistic?

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

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 critical t statistic for the alternative hypothesis, H₁: µ < 12, a 0.005 level of significance, and a sample size of 20 is ______.

The average cost of tuition and 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?

If the null hypothesis is µµ ≥ 200, then a two-tail test is being conducted.

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. Thus, if α = .01, the critical value is ____________.

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. Thus, the alternate hypothesis is ___________________.

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:?

To test the hypothesis that 55% of those families who plan to purchase a vacation residence in Florida want a condominium, the null hypothesis is π = 0.55 and the alternate is π ≠ .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 using the 0.01 level of significance?

Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a mean of 22,100 miles. The fleet owner purchased 18 sets and found that the sample average life was 23,400 miles; the sample standard deviation was 1,412 miles. What is the test statistic?

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

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. The null hypothesis is ______.

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. If α = 0.025, what will be the decision?

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