TABLE 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random sample of 46 cases of light bulbs produced during a morning shift at a plant. A manager wants to know if the mean number of defective bulbs per case is over 20 during the morning shift. She will make her decision using a test with a level of significance of 0.10. The following information was extracted from the Microsoft Excel output for the sample of 46 cases:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: H 0 : μ ≤ 20.000; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
-Referring to Table 9-1, the manager can conclude that there is sufficient evidence to show that the mean number of defective bulbs per case is over 20 during the morning shift with no more than a 5% probability of incorrectly rejecting the true null hypothesis.

Question

Quizplus · Accepted Answer

The table provides information on the one-tail critical values and p-values for different levels of significance and degrees of freedom in a t-test. Based on the information provided in the output from Excel, the manager can reject the null hypothesis at the 0.10 level of significance and conclude that there is sufficient evidence to support the alternative hypothesis, which states that the mean number of defective bulbs per case is greater than 20. The p-value of 0.021 indicates that the probability of obtaining a sample mean of 28 or higher if the true population mean is 20 or lower is less than 0.021, which is lower than the significance level of 0.10. Therefore, the manager can confidently conclude that the mean number of defective bulbs per case is over 20 during the morning shift with no more than a 5% (or 10%) probability of incorrectly rejecting the true null hypothesis.

TABLE 9-1 Microsoft Excel Was Used on a Set of Data Involving