Question

Asked Oct 17, 2019

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.

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:*

*H*_{0} : *p* = 0.15.

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

*Alternative hypothesis:*

*H*_{a} : *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

**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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