It is estimated that the average adult spends $123 in entertainment costs per month. Some believe this figure is too high and conducted a survey of 40 randomly selected adults. They found a mean of $113.03 per month was spent and a standard deviation of $25.99.
-The null and alternative hypotheses to test the claim that the entertainment expenses per month are less than the estimate is _____.

Question

Quizplus · Accepted Answer

The null hypothesis should always represent the equality or status quo and the alternative hypothesis should represent the claim or the research question. Here, the claim is that the entertainment expenses per month are less than the estimate, which implies that the true population mean is less than the estimate. Therefore, the null and alternative hypotheses can be formulated as follows:
Null hypothesis: μ ≥ estimate
Alternative hypothesis: μ < estimate
Since we want to test whether the actual mean is less than the estimate, we choose the left-tailed test, and the appropriate test statistic is the t-test. The null and alternative hypotheses can be written in terms of t as follows:
Null hypothesis: t ≤ t-critical
Alternative hypothesis: t > t-critical
So, the correct null and alternative hypotheses are:
Null hypothesis: μ ≥ 123
Alternative hypothesis: μ < 123
Therefore, the best choice is B.

It Is Estimated That the Average Adult Spends $123 in Entertainment