Question

According to a previous study, the average height of college students was 68 inches in Fall 2005.   We are curious as to whether the average height of college students has changed since 2005. We measure the heights of 50 students who have been randomly selected and find a sample mean of 68.9 inches and standard deviation of 3.2 inches. What conclusions can be made at the 0.05 significance level regarding whether the height of college students has changed since 2005?

Answer 1

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

The null and alternative hypotheses are given as below:

H0: µ = 68 versus Ha: µ ≠ 68

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 = 68

Xbar = 68.9

S = 3.2

n = 50

df = n – 1 = 49

α = 0.05

Critical value = - 2.0096 and 2.0096

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (68.9 - 68)/[3.2/sqrt(50)]

t = 1.9887

P-value = 0.0523

(by using t-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the height of college students has changed since 2005.