Question

The average grade in Math 1530 on test 3 has always been 75. This semester, the average grade on test 3 for 15 students in 1530 was 77.5 with a standard deviation of 5.51. At alpha = 0.10, has the average grade changed for the 3rd test in 1530?

Answer 1

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H₀: The average grade in math is 75.

Alternative hypothesis: H_a: The average grade in math is not 75.

H₀: µ = 75 versus H_a: µ ≠ 75

This is a two tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 75

Xbar = 77.5

S = 5.51

n = 15

df = n – 1 = 14

α = 0.10

Critical value = -1.6450

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (77.5 - 75)/[5.51/sqrt(15)]

t = 0.4348

P-value = 0.6637

(by using t-table)

P-value > α = 0.10

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the average grade has changed for the 3rd test in 1530.