Exam 10: One-Sample Tests of 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, twelve 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?

What is the level of significance?

What type of hypothesis test is indicated if the alternate hypothesis states a direction? ________________________

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 p-value?

A p-value is the same as a stated significance level.

If the null hypothesis is false and the researchers do not reject it, then a Type I error has been made.

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

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 standard deviation?

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?

The probability of a Type II error is directly related to

How is the significance level related to a p-value when the null hypothesis is rejected?

The mean gross annual incomes of certified welders are normally distributed with the mean of $20,000 and a standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $20,000 annually. The alternate hypothesis is that the mean is not $20,000. Which of the following is the alternate hypothesis?

In hypothesis testing, what is the level of significance?

To conduct a test of hypothesis with a small sample, we need to be able to make an assumption that:

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. What is H₁? _____________________

An alternate hypothesis is a statement about a population parameter that is accepted when the null hypothesis is rejected.

The number of trials and the population proportion are respectively represented by what symbols?

How is the significance level related to the size of the test statistic and the probability of a Type I error?

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

The sample proportion is defined as: