Question

In a survey of a SRS of 463 first-year college students the students were asked about studying habits. Among these students the mean response of studying time was 15.3 hours. Suppose we know that study time among similar students varies with standard deviation 8.5 hours. Does this study give statistically significant evidence at the 0.05 significance level that students generally claim to study more than 15 hours per week on average?  For full credit, perform a complete significance test (that is, indicate hypotheses, test statistic, p-value, and state your conclusion).

Answer 1

Null and alternative hypotheses

Ho : = 15

H1 : > 15

Test statistic Z

Z = (xbar - )/(/√n)

Z = ( 15.3 -15)/(8.5/√463)

Z = 0.76

p-value for Z = 0.76 and right tailed test

p-value = P( Z > 0.76)

p-value = 0.2236

Here p-value = 0.2236> 0.05

We fail to reject the null hypothesis

Conclusion : There is no sufficient evidence to support the claim that students generally claim to study more than 15 hours per week on average