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

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

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. =
`(\bar X-\mu)/((s)/(√(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 =
`(25-24)/((2)/(√(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.