Instruction 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.
-Referring to Instruction 9-3,the null hypothesis will be rejected at 5% level of significance.

Question

Quizplus · Accepted Answer

To test the claim, we use a one-tailed t-test with a level of significance of 0.05.
The null hypothesis is that the population mean power consumption is equal to or greater than 250 W, while the alternative hypothesis is that the population mean power consumption is less than 250 W.
Based on the given sample data, we calculate the t-value as:

t = (sample mean - hypothesized mean) / (sample standard error)
t = (257.3 - 250) / (15 / sqrt(20))
t = 2.68

Using a t-table with 19 degrees of freedom (n-1), we find the critical t-value as -1.729.
Since our calculated t-value is greater than the critical t-value and falls in the rejection region, we reject the null hypothesis.
Therefore, the statement "the null hypothesis will be rejected at 5% level of significance" is true.

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