TABLE 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
-True or False: Referring to Table 9-3,the null hypothesis will be rejected at 5% level of significance.

Question

Quizplus · Accepted Answer

To determine if the null hypothesis will be rejected at a 5% level of significance, we need to perform a one-sample t-test using the formula:
t = (x̄ - μ) / (s / sqrt(n))
where x̄ is the sample mean, μ is the hypothesized population mean (in this case, 250 W), s is the sample standard deviation (which we can estimate using the population standard deviation of 15 W), and n is the sample size (20).

Using the values given in the problem, we get:
t = (257.3 - 250) / (15 / sqrt(20)) = 1.71

Using the t-distribution table with 19 degrees of freedom (n-1), and a two-tailed test at a 5% level of significance, we find the critical value to be ±2.093. Since our calculated t-value of 1.71 is within the range of -2.093 to +2.093, we fail to reject the null hypothesis.

Therefore, the answer is false. We cannot reject the claim that the compact microwave oven consumes a mean of no more than 250 W at a 5% level of significance.

TABLE 9-3 An Appliance Manufacturer Claims to Have Developed a Compact Microwave