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

  the correct choice is marked

step-by-step explanation:

the first two graphs show multiple turning points. the last graphs matches the description in every detail.