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. What is the parameter of interest?
2. Can the consumer group conclude that there is enough evidence that the manufacturer’s claim is not true when allowing for a 5% probability of committing a Type I error?

Answer 1

Step-by-step explanation:

Sure, here are the answers to your questions:

1. The parameter of interest is the mean power consumption of the microwave ovens.

2. The consumer group can conclude that there is enough evidence that the manufacturer's claim is not true when allowing for a 5% probability of committing a Type I error.

Here is the explanation:

The parameter of interest is the mean power consumption of the microwave ovens. The manufacturer claims that the mean power consumption is no more than 250 W. The consumer group takes a sample of 20 microwave ovens and finds that they consume a mean of 257.3 W. This is significantly higher than the manufacturer's claim.

The consumer group can use a hypothesis test to determine whether there is enough evidence to conclude that the manufacturer's claim is not true. The null hypothesis is that the mean power consumption is no more than 250 W. The alternative hypothesis is that the mean power consumption is greater than 250 W.

The consumer group can use a z-test to conduct the hypothesis test. The z-score is calculated as follows:

```

z = (x - μ) / σ

```

where:

* z is the z-score

* x is the sample mean (257.3 W)

* μ is the population mean (250 W)

* σ is the population standard deviation (15 W)

The z-score is 3.87. This is greater than the z-score critical value of 1.96, which corresponds to a 5% probability of committing a Type I error.

Therefore, the consumer group can conclude that there is enough evidence to reject the null hypothesis and conclude that the manufacturer's claim is not true. The mean power consumption of the microwave ovens is significantly greater than 250 W.