Question

Do students study less than 150 minutes (2.5 hours), on average, each week? A survey of 51 randomly selected students finds that on average students study 138 minutes per week with a standard deviation of 32 minutes. A hypothesis test based on this data produces a test statistic of -2.68 and a p-value of 0.005. What are the appropriate decision and conclusion at the 5% significance level? Select one or more: Reject the null hypothesis. Do not reject the null hypothesis. There is enough evidence to claim that students study less than 150 minutes, on average, each week. There is not enough evidence to claim that students study less than 150 minutes, on average, each week.

Answer 1

Reject the null hypothesis.

There is enough evidence to claim that students study less than 150 minutes, on average, each week.

Explanation:

Hello!

You have the Hypothesis that "students study less than 150 min, on average, per week"

Symbolically:

H₀:μ≥150

H₁:μ<150

α: 0.05

You have two ways of deciding whether to reject the null hypothesis or not.

With the calculated value: -2.68 (I'll assume this value was obtained under a standard normal distribution)

To take a decision using the statistic value you need to establish the critical region. For this Hypothesis pair, the rejection region is one-tailed to the left. The critical value is
`Z_(0.05) = -1.64`.

If the calculated value is less than -1.64, you reject the null Hypothesis.

If the calculated value is equal to or greater than -1.64, you support the null hypothesis.

Since the calculated statistic (-2.68) is less than -1.64, the decision is to reject the null hypothesis.

-or-

With the p-value 0.005

To take a decision using the p-value, you have to compare it against the significance level.

If the p-value is less than α, then you reject the null hypothesis.

If the p-value is equal or greater than α, you support the null hypothesis.

Since the given p-value is less than the significance level, you reject the null hypothesis.

I hope you have a SUPER day!