A recent report stated that less than 35 percent of adult residents in a certain city will be able to pass a physical fitness test. Consequently, the city's Recreation Department is trying to convince the City Council to fund more physical fitness programs. The council is facing budget constraints and is skeptical of the report. The council will fund more physical fitness programs only if the Recreation Department can provide convincing evidence that the report is true. The Recreation Department plans to collect data from a sample of 185 adult residents in the city. A test of significance will be conducted at a significance level of a= 0.05 for the following hypotheses.
H0:p=0.35
Ha:p<0.35
where p is the proportion of adult residents in the city who are able to pass the physical fitness test.
The Recreation Department recruits 185 residents who volunteer to take the physical fitness test. The test is passed by 77 of the 185 volunteers, indicating that more than 35 percent of the city is in shape. Describe the primary flaw in the study described in part and explain why it is a concern.
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rafikiedu08 2 weeks ago
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The primary flaw is that the sample will slightly overestimate the physical fitness of the people of the town.

The given  hypothesis are,

Type II error is accepted in null hypothesis when it is not actually true.

In the given question null hypothesis p= 0.35

The conclusion is that in the given sample proportion is  not equal to 0.35, though we know that proportion is not equal to 0.35 we accept the null hypothesis, that is wrong.

Now given n=185,x=77 P=0.53 then Q=1-0.35=0.65

Now test statistic

Solving for Z using the given values we get :

Z=1.99

Now 1.99>-1.65

So we accept

The primary flaw in the system is that the sample is not randomly selected rather they are volunteers. So it is reasonable to think that the physical fitness of the town will be slightly over estimated by the experiment.

To learn more about sample of an experiment:

https://brainacademy.pro/question/24466382

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