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. The test statistic is
A) 1.96.
B) 2.50.
C) 1.65.
D) .05.

Question

Quizplus · Accepted Answer

We need to conduct a one-sample t-test with the null hypothesis being that the population mean age is 24 and the alternative hypothesis being that it is greater than 24. Using the formula for the t-test: 
t = (x̄ - μ) / (s / sqrt(n))
where x̄ is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size. 
Plugging in the given values, we get:
t = (25 - 24) / (2 / sqrt(25)) = 2.5
From the t-distribution table with degrees of freedom (df) = n-1 = 24, and a significance level of 0.05 for a one-tailed test, the critical value is 1.711. Since our calculated t-value (2.5) is higher than the critical value (1.711), we reject the null hypothesis and conclude that there is sufficient evidence to say that the average age of all the students at the university is significantly more than 24. Therefore, the correct answer is B.

A Random Sample of 25 Students Selected from the Student