Question

A professional sports league claims that the average age of players in the league is 28 years old. A random sample of 20 players in the league was selected, and their ages are recorded in the following table.

Use Excel to test whether the mean player age is different from 28 years old, and then draw a conclusion in the context of the problem. Use α=0.05.

Age (years)
32
28
29
32
33
28
31
28
30
28
29
34
30
30
31
30
28
21
32
29

Select the correct answer below:

Reject the null hypothesis. There is sufficient evidence to conclude that the mean is not equal to 28.

Reject the null hypothesis. There is insufficient evidence to conclude that the mean is not equal to 28.

Fail to reject the null hypothesis. There is sufficient evidence to conclude that the mean is not equal to 28.

Fail to reject the null hypothesis. There is insufficient evidence to conclude that the mean is not equal to 28.

Answer 1

let us consider the null and alternative hypothesis is

Ho :

Ha:

using excel>addin>phstat>one sample t

we have

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	28
Level of Significance	0.05
Sample Size	20
Sample Mean	29.65
Sample Standard Deviation	2.719810365
Intermediate Calculations
Standard Error of the Mean	0.608168086
Degrees of Freedom	19
t Test Statistic	2.713065742
Two-Tail Test
Lower Critical Value	-2.093024054
Upper Critical Value	2.093024054
p-Value	0.013794667
Reject the null hypothesis

p value is 0.014 which is less than 0.05 so we reject Ho

Reject the null hypothesis. There is sufficient evidence to conclude that the mean is not equal to 28.