Question

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

Answer #1

Solution:

The null and alternate hypotheses are

H_{0}: μ_{1} = μ_{2}; H_{1}:
μ_{1} ≠ μ_{2}

Two tailed test.

The test statistic is

z =

= (22.12 - 22.56)/[(3.68^{2}/50)
+ (4.7^{2}/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 H_{0}

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

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