Question

A lower proportion of males ages 25 to 44 visited the gym than the proportion of males ages 45 to 64. The table below provides the numbers by age group. Test at the 2% level of signifcance.
	25 - 44	45 - 64
Visited the gym	7	33
Did not visit the gym	9	50
a. State the Null Hypothesis
b. State the Alternative Hypothesis
c. Is this a right-tailet, left-tailed or a two-tailed test?
d. State the distribution to use for the test
e. What is the test statistic (z value)?
f. What is the p value?
g. At 95% what is my significance level (alpha):
h. Decision:
i. Reason for decision:
j. Conclusion:

Answer 1

Let the age group 25-44 be 1st group and age group 45-64 is 2nd group.

A.

H₀: p₁ = p₂

B.

H₁: p₁ < p₂

C.

Left Tailed test

D.

Normal Distribution

E.

= 9/16

= 0.5625

= 33/83

= 0.3973

= (9+33)/(16+83)

= 0.4242

Test Statistic Calculation:

F.

p-value = 0.8892

G.

At 95% signficance level is 0.05

H.

Do not reject the null hypothesis.

I.

Since p-value = 0.8892 > 0.02 i.e. we can not reject the null hypothesis.

J.

Thus we can say that there is not enough evidence to conclude that a lower proportion of males aged between 25-44 visit the gym as compared to the males in the age group 45-64.

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