Exam 10: One-Sample Tests of Hypothesis

A p-value is a probability.

For a one-tailed test with a 0.05 level of significance, the critical z statistic is 1.645, but the critical t statistic is 1.96.

A test statistic is computed using ________________ information.

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 are the degrees of freedom?

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 test statistic for this test?

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

If the null hypothesis is false and the researchers accept it, a _______ error has been made.

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 alternate hypothesis?

If the null hypothesis is true and the researchers reject it, a ________ error has been made.

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 computed z statistic is ______________.

The average cost of tuition and 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. The population standard deviation is $1,200. Let α = 0.05. What is the p-value for this test?

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

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?

Which symbol represents a test statistic used to test a hypothesis about a population mean?

A random sample of 400 families who planned to buy a vacation residence revealed that 228 families want to buy a condominium in Florida. At the 0.01 significance level, test the statement that 55% of those families who plan to purchase a vacation residence in Florida want a condominium. To decide if the sample data support the 55%, state your decision in terms of the null hypothesis. Use a 0.01 level of significance.

The waiting time for patients at a 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 the waiting time is less than 15 minutes. The quality-assurance department sampled 50 patients and found that the mean waiting time was 14.25 minutes. For a significance level of 0.05, what is the critical value?

The mean annual incomes of certified welders are normally distributed with the mean of $50,000 and a standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. If the level of significance is 0.10, what is the critical value?

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 decision for a statistical significant change in average weights at birth at the 5% level of significance?

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?

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