Question

Students are expected to have higher grades if they spend more time studying. An educational theorist collects data on 22 students and the number of hours they spend studying is:

In R: hours <- c(22.3, 22.8, 21.7, 21.3, 18.5, 20.2, 20.7, 18.2, 22.9, 21.5, 18.1, 19.8, 22.7, 22.9, 19.3, 20.8, 21.1, 18.8, 22.4, 18.2, 20, 23) Their grade average is: grades <- c(8.6, 8.5, 7.8, 9.1, 8, 10.2, 7.4, 8.8, 8.8, 8, 8.3, 8.8, 9.8, 9.1, 9.4, 7.4, 10.2, 7.1, 10.4, 7, 9.2, 10.7)

Is there evidence that students who spend more hours studying score higher grades?

(a) State a sensible null hypothesis

(b) State the precise definition of p-value and explain what “more extreme” means in this context

(c) Is a one-sided or two-sided test needed? justify

(d) Perform a linear regression using R and interpret

Answer 1

(d)

As the p-value for hours is 0.0449 < 0.05, we reject the null hypothesis. Hence the regression of grades over hours of study is significant at 5% significance level. But at the same time, if a 1% siginficance level is considered then we'll have to accept the null hypothesis and say that the regression is insignificant.

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