Exam 10: One-Sample Tests of Hypothesis

Type II error is the probability or risk of rejecting a null hypothesis when it is actually true.

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 critical value for $\alpha$ = 0.025?

Among one hundred people surveyed, sixty-six people or 0.33 preferred the product. What is the 0.33 called? ________________

A manufacturer claims that less than 1% of all his products do not meet the minimum government standards. A survey of 500 products revealed ten did not meet the standard. What is the p-value? _______________

The probability of a Type I error is also referred to as alpha.

If the null hypothesis is true and the researchers reject it, what error has been made? __________

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 critical value if the level of significance is 0.10?

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 decision rule? ______________

Hypothesis testing is a procedure that uses sample evidence and probability theory to decide whether to reject or fail to reject a 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 variance?

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 degree of freedom?

The waiting time for patients at 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 found in a sample of 50 patients that the mean waiting time was 14.25 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 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 1.784. To decide if the sample data support the claim that mean length is 43 millimeters, state your decision in terms of the null hypothesis. Use a 0.02 level of significance.

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 and a standard deviation of 1.2019. 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 null hypothesis makes a claim about a

The average cost of tuition, room and board at small private liberal arts colleges 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 with a standard deviation of $1,200. Let = 0.05. What is the critical z-value for this test?

The waiting time for patients at local walk-in health clinic follows a normal distribution with a mean of 15 minutes and a population standard deviation of 5 minutes. The clinic wants to know if waiting time is less than 15 minutes. The quality-assurance department found in a sample of 50 patients that the mean waiting time was 14.25 minutes. For a significance level of 0.05, what is the critical value?

To decide if a null hypothesis should be rejected, a ____________ is compared to the critical value.

If we reject the null hypothesis, what can we conclude subject to the $\alpha$ risk?

If the critical z-value for a test statistic equals 2.45, what value of the test statistic would provide the least chance of making a Type I error?