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.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.

Question

Quizplus · Accepted Answer

We can use a one-sample t-test to determine if the sample mean age is significantly different from 24. The null hypothesis is that the population mean age is 24 and the alternative hypothesis is that the population mean age is greater than 24. With a sample size of 16 and a standard deviation of 2, the t-statistic is calculated as (25-24)/(2/sqrt(16)) = 4. The degrees of freedom for the test are 15 (n-1). Using a t-table or calculator with α = .05 and 15 degrees of freedom, the critical value for a one-tailed test is 1.753. Since our calculated t-statistic (4) is greater than the critical value (1.753), we reject the null hypothesis and conclude that the population mean age is significantly more than 24. Therefore, the answer is D.

A Random Sample of 16 Students Selected from the Student