Question

1. A research report from the Center for Disease Control (CDC) showed that 49.4% of Americans aged 18+ years meet their Physical Activity Guidelines for aerobic physical activity. A random sample of 41 members of a national gym chain found that 28 met the CDC’s guidelines.

1. Test at the 0.01 level whether the percentage of their gym members meeting the guidelines is better.
2. Do the results of your test place the gym chain in a favorable or unfavorable light? Explain.
3. Describe a Type I error in context

Answer 1

Ans:

a)

H₀:p=0.494

H_a:p>0.494

sample proportion=28/41=0.6829

Test statistic:

z=(0.6829-0.494)/SQRT(0.494*(1-0.494)/41)

z=2.42

p-value=P(z>2.42)=0.0078

As,p-value<0.01,we reject the null hypothesis.

There is sufficient evidence to support the claim that the percentage of their gym members meeting the guidelines is better.

b)Yes,the results of your test place the gym chain in a favorable light.

c)

when we conclude that percentage of your gym members meeting the guidelines is better than 49.4%,but in fact,it is not better than 49.4%(i.e.when we reject the null hypothesis and null hypothesis is true)