Question

A critical factor in choosing a location for a new clothing store is the average clothing expenditure per household in the area. A survey of 25 randomly chosen households in a particular area yielded a mean and standard deviation of annual expenditure on clothes of $385 and $60 respectively.

Can you test whether, at the 5% level of significance, the population mean annual expenditure on clothing in this area is less than $400?

Answer 1

To test whether the population mean annual expenditure on clothing in this area is less than $400, we can use a one-sample t-test. The test statistic (-1.25) is compared to the critical value from the t-distribution table at the desired level of significance (5%). We fail to reject the null hypothesis, meaning there is not enough evidence to conclude that the population mean annual expenditure on clothing in this area is less than $400.

Step-by-step explanation:

To test whether the population mean annual expenditure on clothing in this area is less than $400, we can use a one-sample t-test. First, we need to state the null hypothesis and the alternative hypothesis:

• Null hypothesis: The population mean annual expenditure on clothing is $400 or more.
• Alternative hypothesis: The population mean annual expenditure on clothing is less than $400.

Next, we calculate the test statistic using the formula:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Substituting the given values into the formula, we have:

t = (385 - 400) / (60 / sqrt(25)) = -15 / (60 / 5) = -15 / 12 = -1.25

Finally, we compare the test statistic to the critical value from the t-distribution table at the desired level of significance (5%).

Since the test statistic (-1.25) is not less than the critical value, we fail to reject the null hypothesis. This means there is not enough evidence to conclude that the population mean annual expenditure on clothing in this area is less than $400.