A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. At 95% confidence, test to determine if the average age of all the students at the university is significantly more than 24.

The degrees of freedom are:

Now since we are conducting a right tailed test the p value can be calculated as follows:

Since the p value is lower than the significance level of we have enough evidence to conclude that the true mean for the ages is significantly higher than 24

Step-by-step explanation:

Information provided

represent the mean for the ages

represent the sample standard deviation

sample size  

represent the value to check

represent the significance level

t would represent the statistic

represent the p value

Hypothesis to verify

We want to check if the average age of all the students at the university is significantly more than 24, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

Since we don't know the population deviation the statistic would be given by:

(1)  

Replacing the data given we got:

The degrees of freedom are:

Now since we are conducting a right tailed test the p value can be calculated as follows:

Since the p value is lower than the significance level of we have enough evidence to conclude that the true mean for the ages is significantly higher than 24