MATH SOLVE

4 months ago

Q:
# 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. What is the critical value with a level of significance of 0.05 and what is the test statistic and what is the p value?

Accepted Solution

A:

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 [tex]\mu[/tex] = mean power consumption for microwave ovens.So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 250 W {means that a compact microwave oven consumes a mean of no more than 250 W}Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 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. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)where, [tex]\bar X[/tex] = sample mean power consumption for ovens = 257.3 W σ = population standard deviation = 15 W n = sample of microwave ovens = 20So, the test statistics = [tex]\frac{257.3-250}{\frac{15}{\sqrt{20} } }[/tex] = 2.176The 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.