Question

n appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 260 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 265 W. The value of the test statistic is ________.


2.18


-1.58


1.49


-2.45

Answer 1

To calculate the test statistic, we can use the formula for the z-test:

\[
z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}
\]

Where:
- \(\bar{x}\) = sample mean
- \(\mu\) = population mean under the null hypothesis
- \(\sigma\) = population standard deviation
- \(n\) = sample size

From the problem:
- Sample mean (\(\bar{x}\)) = 265 W
- Population mean (\(\mu\)) = 260 W
- Population standard deviation (\(\sigma\)) = 15 W
- Sample size (\(n\)) = 20

Now, substituting in the values:

\[
z = \frac{265 - 260}{15 / \sqrt{20}}
\]

First, we calculate the standard error (SE):

\[
SE = \frac{15}{\sqrt{20}} \approx \frac{15}{4.472} \approx 3.354
\]

Now, substituting back into the formula for z:

\[
z = \frac{5}{3.354} \approx 1.49
\]

Thus, the value of the test statistic is approximately **1.49**.