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

a. State the Null Hypothesis

( Equal or higher proportion of males ages 25 to 44 visited the gym than the proportion of males ages 45 to 64.)

b. State the Alternative Hypothesis

( A lower proportion of males ages 25 to 44 visited the gym than the proportion of males ages 45 to 64.)

c. Is this a right-tailet, left-tailed or a two-tailed test?

left-tailed

d. State the distribution to use for the test

Z distribution

e. What is the test statistic (z value)?

n1 = 16

p1 = 7/16 = 0.4375

n2 = 83

p2 = 33/83 = 0.3976

Test Statistic (Z value) is given by:

So,

Test Statistic (Z value) = 0.298

f. What is the p value?

By Technology, p value = 0.6171

So,

p value = 0.6171

g. At 95% what is my significance level (alpha):

= 0.05

h. Decision:

Fail to reject null hypothesis

i. Reason for decision:

Since p value = 0.6171 is less than = 0.05, the difference is not significant.

j. Conclusion:

The data do not support the claim that a lower proportion of males ages 25 to 44 visited the gym than the proportion of males ages 45 to 64.