A class survey in a large class for first-year college students asked, “About ho

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 463 students was x = 118 minutes. Suppose we know that distribution of study times follows a Normal distribution with standard deviation = 65 minutes. 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 less than 2 hours per night on the average?

(a) State the null and alternative hypotheses in terms of the mean study time in min- utes for the population.

(b) What is the value of the test statistic?

(c) What is the P-value of the test? Can you conclude that the students do claim to study less than 2 hours per weeknight on the average?

Explanation / Answer

Part-a

Null Hypothesis H0:µ=120 minutes

Alternative Hypothesis H0:µ<120 minutes (2 hours)

Part-b

Test statistic Z=(xbar-120)/(/sqrt(n))

=(118-120)/(65/sqrt(463))

=-0.6621

Part-c

p-value=P(Z<-0.6621)=0.254 using excel function =NORMSDIST(-0.6621)

As p-value is larger than even 0.10 level of significance , so we have not enough evidence to reject the null hypothesis and conclude that the claim of students that they study less than 2 hours is false.

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