Exam 10: Hypothesis Testing

The local pharmacy prides itself on the accuracy of the number of tablets that are dispensed in a 60-count prescription. The new manager feels that the pharmacy assistants might have become careless in counting due to an increase in the volume of prescriptions. To test her theory, she randomly selects 40 prescriptions requiring 60 tablets and recounts the number in each bottle. She finds a sample mean of 62.05 and a standard deviation of 4.45. Calculate the test statistic for using the critical value rule testing that the number of tablets is significantly different from 60.

It has been hypothesized that on average employees spend one hour a day playing video games at work. To test this at her company, a manager takes a random sample of 35 employees, who showed a mean time of 55 minutes per day with an assumed population standard deviation of 5 minutes. Calculate a confidence interval to test the hypotheses that the employees spend a different amount of time from one hour (60 minutes) at α = .02 and interpret.

Everything else being constant, increasing the sample size decreases the probability of committing a Type II error.

When applying either the critical value rule or the p-value rule about a single mean, other relevant factors held constant, increasing the level of significance, α, from .05 to .10 will reduce the probability of a Type II error.

The value of χ²_α in a particular situation depends on

In a bottling process, a manufacturer will lose money if the bottles contain either more or less than is claimed on the label. Suppose a quality manager for a steak sauce company is interested in testing whether the mean number of ounces of steak sauce per restaurant-size bottle differs from the labeled amount of 20 ounces. The manager samples nine bottles, measures their contents, and finds the sample mean is 19.7 ounces and the sample standard deviation is .3 ounces. Calculate the appropriate test statistic.

The exact shape of the chi-square distribution depends on the degrees of freedom.

The manager of a grocery store wants to determine whether the amount of water contained in 1-gallon bottles purchased from a nationally known manufacturer actually averages 1 gallon. It is known from the specifications that the standard deviation of the amount of water is equal to .02 gallon. A random sample of 32 bottles is selected, and the mean amount of water per 1-gallon bottle is found to be .995 gallon. Calculate a confidence interval to test the hypotheses at α = .001 and determine whether the specifications are being met.

When the null hypothesis is not rejected, there is no possibility of making a Type I error.

In a study of distances traveled by buses before the first major engine failure, a sample of 191 buses results in a mean of 96,700 miles and a population standard deviation of 37,500 miles. Calculate the p-value corresponding to the test statistic used to test the claim that the mean distance traveled before a major engine failure is more than 90,000 miles and, applying the p-value rule, determine if the null hypothesis can be rejected at α = .01.