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ANEK [815]
3 years ago
11

A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standar

d 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
Mathematics
1 answer:
ss7ja [257]3 years ago
8 0

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 = <u><em>true average age of all the students at the university.</em></u>

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 <u>One-sample t-test statistics</u> 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, <u><em>the test statistics</em></u> =  \frac{25-24}{\frac{2}{\sqrt{16} } }  ~  t_1_5  

                                     =  2  

The value of t-test statistics is 2.

<u>Also, the P-value of test-statistics is given by; </u>

            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.

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