Suppose that between their first and second years in college, 400 students are randomly selected and given a university grant to purchase a new computer.

Suppose that between their first and second years in college, 400 students are randomly selected and given a university grant to purchase a new computer. For student i, yi denotes the change in GPA from the first year to the second year. If the average change is y̅ = .132 with standard deviation s = 1.27, is the average change in GPAs statistically greater than zero?

Expert Solution

Null and alternative hypotheses:

Ho: µ = 0

Ha: µ > 0

Test statistic

t = 0.132 – 0/(1.27/√100)

t = 1.039

Degrees of freedom = n - 1 = 100 - 1 = 99

Hence,

p - Value = P(t99 > 1.039) = 0.1506

Since this p - value is quite large, we do not reject the null hypothesis. Hence,

We do not have sufficient evidence to conclude that the average change in GPAs are statistically greater than zero.

Junaid answered 2 years ago

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