Question

# a professor at University wants to see whether there is a significant difference in ages of...

a professor at University wants to see whether there is a significant difference in ages of resident students and commuting students. he selects random sample of 50 students from each group. the average age of residents students is X1= 22.12 years and the average age of commuter students is x 2 = 22.56 years. at Alpha= 0.05,decide if there is enough evidence to reject the claim of no difference in the ages of the two groups. assume mean1=3.68 and mean 2=4.7

Solution:

The null and alternate hypotheses are

H0: μ1 = μ2; H1: μ1 ≠ μ2

Two tailed test.

The test statistic is

z = = (22.12 - 22.56)/ [(3.682/50) + (4.72/50)]

= -0.52

Test statistic z = -0.52

For two tailed test ,

p value = P(Z < -z) + P(Z > +z) = P(Z < -0.52) + P(Z > +0.52) = 0.3015 + 0.3015 = 0.603

p value is greater than the level of significance 0.05

Fail to reject H0

There is not enough evidence to reject the claim of no difference in the ages of the two groups.

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