Question

At a certain university the average freshman had a high school average of 88, standard deviation = 3

In 1987, a sample of 100 freshman had a mean high school average of 86.5

Is this a change in freshman average?

Answer 1

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

The null and alternative hypotheses are given as below:

H0: µ = 88 versus Ha: µ ≠ 88

This is a two tailed test.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 88

Xbar = 86.5

σ = 3

n = 100

α = 0.05

Critical value = -1.96 and 1.96

(by using z-table or excel)

Z = (86.5 - 88)/[3/sqrt(100)]

Z = -5.00

P-value = 0.0000

(by using Z-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that there is a change in freshman average.