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The auditor for a large corporation routinely monitors cash disbursements. As part of this process, the auditor examines check request forms to determine whether they have been properly approved. Improper approval can occur in several ways. For instance, the check may have no approval, the check request might be missing, the approval might be written […]

The Chi-Square Distribution (Optional) Sometimes we can make statistical inferences by using the chi-square distribution. The probability curve of the χ2 (pronounced chi-square) distribution is skewed to the right. Moreover, the exact shape of this probability curve depends on a parameter that is called the number of degrees of freedom (denoted df). Figure 9.14 illustrates

What happens to the power of the test as the alternative value of μ moves away from 60? The power curve for a statistical test is a plot of the power = 1 − β on the vertical axis versus values of μ that make the null hypothesis false on the horizontal axis. Plot the

Explain why we are able to compute many different values of β, the probability of a Type II error, for a single hypothesis test. 9.78 Explain what is meant by a A serious Type II error. b The power of a statistical test. 9.79 In general, do we want the power corresponding to a serious

When is it important to know the probability of a Type II error? Calculating the Sample Size Needed to Achieve Specified Values of α and β Assume that the sampled population is normally distributed, or that a large sample will be taken. Consider testing H0: μ = μ0 versus one of Ha: μ > μ0,

Calculating the Sample Size Needed to Achieve Specified Values of α and β Assume that the sampled population is normally distributed, or that a large sample will be taken. Consider testing H0: μ = μ0 versus one of Ha: μ > μ0, Ha: μ < μ0, or Ha: μ ≠ μ0. Then, in order to make the

The Valentine’s Day Chocolate Case In the Valentine’s Day chocolate case we are testing H0: μ = 330 versus Ha: μ ≠ 330 by setting α = .05. We have seen that the mean of the reported order quantities of a random sample of n = 100 large retail stores is . Assuming that σ equals 40,

Calculating the Probability of a Type II Error Assume that the sampled population is normally distributed, or that a large sample will be taken. Consider testing H0: μ = μ0 versus one of Ha: μ > μ0, Ha: μ < μ0, or Ha: μ ≠ μ0. Then, if we set the probability of a Type I error

Do you think the results of the consumer group’s survey have practical importance? Do you think the results of the consumer group’s survey have practical importance? Explain your opinion. 9.5: Type II Error Probabilities and Sample Size Determination (Optional) Chapters 9 and 11 As we have seen, we usually take action (for example, advertise a