Question

1. A group of medical researchers knew from previous studies that in the past, about 39% of all men between 45 and 59 were regularly active. Researchers were concerned that this percentage has declined over time. They selected a random sample of 1927 men in this age group and interviewed them. 680 said they were regularly active.

Perform a full hypothesis test at the α = 0.05 level. (write out the hypothesis, determine the test statistic, p-value, and write out the conclusion in full sentences):

Answer 1

H0: p = 0.39

Ha: p < 0.39

Sample proportion = 680 / 1927 = 0.3529

Test statistics

z = ( - p) / sqrt [ p(1 - p) / n]

= (0.3529 - 0.39) / Sqrt ( 0.39 ( 1 - 0.39) / 1927)

= -3.34

p-value = P(Z < z)

= P(Z < -3.34)

= 0.0004

Since p-value < 0.05 level, reject H0.

We conclude at 0.05 level that we have sufficient evidence to conclude that percentage has declined over time.