Question

You are testing the claim that the mean GPA of night students is less than the mean GPA of day students. You sample 45 night students, and the sample mean GPA is 2.66 with a standard deviation of 0.91 You sample 60 day students, and the sample mean GPA is 2.7 with a standard deviation of 0.98 Use the t-distribution to calculate the test statistic, rounded to 2 decimal places

Answer 1

H0: night >= day

Ha: night < day

Pooled standard deviation Sp = Sqrt [ (n1-1) S²night + (n2 - 1 ) S²day / n1 + n2 - 2 ]

= sqrt [ (45-1) * 0.91² + (60-1) 0.98² / 60+45 - 2]

= 0.9507

Test statistics

t = (night - day) / [Sp * Sqrt ( 1 / n1 + 1 / n2) ]

= (2.66 - 2.7) / [ 0.9507 * sqrt( 1 / 45 + 1 / 60 ) ]

= -0.21