Question

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 p-value is between

Answer 1

Answer:

The P-value is between 2.5% and 5% from the t-table.

Step-by-step explanation:

We are given that 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.

Let $\mu$ = true average age of all the students at the university.

So, Null Hypothesis, $H_0$ : $\mu \leq$ 24 years     {means that the average age of all the students at the university is less than or equal to 24}

Alternate Hypothesis, $H_A$ : $\mu$ > 24 years     {means that the average age of all the students at the university is significantly more than 24}

The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;

                               T.S.  =  $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$  ~   $t_n_-_1$

where, $\bar X$ = sample average age = 25 years

             s = sample standard deviation = 2 years

             n = sample of students = 16

So, the test statistics =  $\frac{25-24}{\frac{2}{\sqrt{16} } }$  ~  $t_1_5$  

                                     =  2  

The value of t-test statistics is 2.

Also, the P-value of test-statistics is given by;

            P-value = P( $t_1_5$ > 2) = 0.034 {from the t-table}

The P-value is between 2.5% and 5% from the t-table.