Question

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. 1) The appropriate hypotheses to determine if the manufacturer's claim appears reasonable are H subscript 0 colon________ and H subscript 1 colon________. (2 points) 2) For a test with a level of significance of 0.05, the critical value would be ________. (2 point) 3) The value of the test statistic is ________. (4 points) 4) Is there evidence that a compact microwave oven consumes a mean of no more than 250 W? (2 points)

Answer 1

Answer:

We conclude that a compact microwave oven consumes a mean of more than 250 W.

Step-by-step explanation:

We are given that an appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W with a population standard deviation of 15 W.

They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.

Let $\mu$ = mean power consumption for microwave ovens.

So, Null Hypothesis, $H_0$ : $\mu$ $\leq$ 250 W     {means that a compact microwave oven consumes a mean of no more than 250 W}

Alternate Hypothesis, $H_A$ : $\mu$ > 250 W     {means that a compact microwave oven consumes a mean of more than 250 W}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

                                T.S. =  $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$  ~ N(0,1)

where, $\bar X$ = sample mean power consumption for ovens = 257.3 W

            σ = population standard deviation = 15 W

            n = sample of microwave ovens = 20

So, the test statistics  =  $\frac{257.3-250}{\frac{15}{\sqrt{20} } }$

                                      =  2.176

The value of z test statistics is 2.176.

Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.

Since our test statistic is more than the critical value of t as 2.176 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that a compact microwave oven consumes a mean of more than 250 W.