A class survey in a large class for first-year college students asked, \"About h

Question

A class survey in a large class for first-year college students asked, "About how many minutes do you study on a typical weeknight?" The mean response of the 282 students was x¯ = 146 minutes. Suppose that we know that the studey time follows a Normal distribution with standard deviation = 65 minutes in the population of all first-year students at this university. Regard these students as an SRS from the population of all first-year students at this university. Does the study give good evidence that students claim to study more than 2 hours per night on the average?

(a) State null and alternative hypotheses in terms of the mean study time in minutes for the population.
(b) What is the value of the test statistic z?
(c) Can you conclude that students do claim to study more than two hours per weeknight on the average?

Explanation / Answer

Solution:-

a) State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: < 120

Alternative hypothesis: > 120

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample z-test.

Analyze sample data. Using sample data, we compute the standard error (SE), z statistic test statistic (z).

SE = s / sqrt(n)

S.E = 3.87

b)

z = (x - ) / SE

z = - 6.72

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a z statistic test statistic of - 6.72.

Thus the P-value in this analysis is less than 0.0001.

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.

c) From the above test we have sufficient evidence in the favor of the claim to study more than two hours per weeknight on the average.

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