# In a recent study, researchers found that 40 out of 250 boys aged 7-13 were overweight or obese. On the basis of this study can we conclude that more than 15% of the boys aged 7-13 in the sampled population are overweight or obese? Use a 5% level of significance.1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic, and 5) your conclusion including a comparison to alpha or the critical value.

Question

In a recent study, researchers found that 40 out of 250 boys aged 7-13 were overweight or obese. On the basis of this study can we conclude that more than 15% of the boys aged 7-13 in the sampled population are overweight or obese? Use a 5% level of significance.

1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic, and 5) your conclusion including a comparison to alpha or the critical value.

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Step 1

1) Stating the appropriate null and alternative hypotheses:

Based on the study, it was found that 15% of the boys aged 7-13 were overweight or obese. The experiment found that 40 out of the 250 boys aged 7-13 were overweight or obese.

Let p be the proportion of boys aged 7-13 were overweight or obese.

The hypotheses are given below:

Null hypothesis:

H0 : p = 0.15.

That is, the proportion of boys aged 7-13 were overweight or obese is 0.15.

Alternative hypothesis:

Ha : p > 0.15.

That is, the proportion of boys aged 7-13 were overweight or obese is greater than 0.15.

Step 2

2) Since the data deals with proportion, the z-test for proportion can be used for the testing.

Step 3
1. Decision rule:

If test statistics value is greater than critical value then reject the null hypothesis. Otherwise fail to reject the n...

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