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.The test statistic is
A) 1.96.
B) 2.00.
C) 1.65.
D) .05.

Question

Quizplus · Accepted Answer

We can perform a one-sample t-test with the null hypothesis: the population mean age is equal to 24, and the alternative hypothesis: the population mean age is greater than 24.

The test statistic is: 
t = (sample mean - hypothesized population mean) / (standard error) 
where the standard error = standard deviation / square root of sample size
    = 2 / sqrt(16)
    = 0.5

t = (25 - 24) / 0.5 = 2

The degrees of freedom for this test are 15 (n-1), which we can use to look up the critical value of t for a one-tailed test at the 0.05 significance level. Using a t-table or calculator, we find the critical value to be 1.753.

Since the calculated t-value (2) is greater than the critical t-value (1.753), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the average age of all the students at the university is significantly more than 24.

A Random Sample of 16 Students Selected from the Student