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 1% level of significance.

Question

Quizplus · Accepted Answer

To determine if the null hypothesis will be rejected at a 1% level of significance, we need to conduct a one-tailed hypothesis test.

Null hypothesis: μ ≤ 250 
Alternative hypothesis: μ > 250

We will use the z-test because we have a sample size greater than 30 and know the population standard deviation.

z = (x̄ - μ) / (σ / √n) 
z = (257.3 - 250) / (15 / √20) 
z = 3.09

Using a z-table or calculator, the probability of obtaining a z-score of 3.09 or higher is less than 0.01, which means that the result is statistically significant at the 1% level of significance.

However, since the alternative hypothesis is μ > 250, we should reject the null hypothesis and conclude that the claim of the manufacturer is not supported by the sample data, meaning that the microwave ovens consume more than 250 W on average. Therefore, the correct answer is B.

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