A random sample of 25 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years.We want to determine if the average age of all the students at the university is significantly more than 24.Assume the distribution of the population of ages is normal.Using α = .05, it can be concluded that the population mean age is

A) not significantly different from 24.
B) significantly different from 24.
C) significantly less than 24.
D) significantly more than 24.

We need to conduct a one-sample t-test to determine if the sample mean age of 25 is significantly different from 24. We can use a t-test because we do not know the population standard deviation.

Our null hypothesis is that the population mean age is equal to 24, and our alternative hypothesis is that the population mean age is greater than 24.

We can calculate the t-statistic using the formula:

t = (sample mean - hypothesized population mean) / (standard error of the mean)

The standard error of the mean is calculated as:

SE = S / sqrt(n)

Where S is the sample standard deviation, and n is the sample size.

Plugging in our values:

t = (25 - 24) / (2 / sqrt(25)) = 2.5

With 24 degrees of freedom (n-1), we can look up the critical t-value at alpha = .05 using a t-distribution table. For a one-tailed test, the critical t-value is 1.711.

Since our calculated t-value of 2.5 is greater than the critical t-value of 1.711, we reject the null hypothesis and conclude that the population mean age is significantly greater than 24.