Question

The administration of a local college states that the average age of its students is 28 years. Records of a random sample of 100 students give a mean age of 31 years. Using a population standard deviation of 10 years, test at the 5% significance level whether there is evidence that the administration’s statement is incorrect.

State clearly your null and alternative hypotheses.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 28

H_a : 28

= 31

= 28

= 10

n = 28

Test statistic = z = ( - ) / / n

= (31 - 28) / 10 / 28 = 1.59

Test statistic = 1.59

P(z > 1.59) = 1 - P(z < 1.59) = 1 - 0.9441 = 0.0559

P-value = 2 * P(z > 1.59) = 2 * 0.0559 = 0.1118

= 5% = 0.05

P-value >

Fail to reject the null hypothesis .

There is no evidence that the administration’s statement is incorrect .