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. The appropriate hypotheses to determine if the manufacturer's claim appears reasonable are

Answer 1

Null Hypothesis,
`H_0` :
`\mu \leq` 250 W

Alternate Hypothesis,
`H_A` :
`\mu` > 250 W

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.

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

Let
`\mu` = mean power consumption of microwave ovens.

So, Null Hypothesis,
`H_0` :
`\mu \leq` 250 W

Alternate Hypothesis,
`H_A` :
`\mu` > 250 W

Here, null hypothesis states that the mean power consumption of microwave ovens is no more than 250 W.

On the other hand, alternate hypothesis sates that the mean power consumption of microwave ovens is more than 250 W.

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

T.S. =
`(\bar X-\mu)/((\sigma)/(√(n) ) )` ~ N(0,1)

Hence, this would be the appropriate hypotheses to determine if the manufacturer's claim appears reasonable.