Mathematics, 16.03.2020 23:30 lexybellx3

In a recent study, researchers found that 31 out of 150 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. Give each of the following to receive full credit: 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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Answer from: alleyeverett031

1) Null hypothesis: $p \leq 0.15$

Alternative hypothesis: p 0.15

2) The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value p_o .

3) $z_{crit}= 1.64$

And the rejection zone would be z1.64

4) Calculate the statistic

$z=\frac{0.207 -0.15}{\sqrt{\frac{0.15(1-0.15)}{150}}}=1.955$

5) Statistical decision

For this case our calculated value is on the rejection zone, so we have enough evidence to reject the null hypothesis at 5% of significance and we can conclude that the true proportion is higher than 0.15

Step-by-step explanation:

Data given and notation

n=150 represent the random sample taken

X=21 represent the boys overweight

$\hat p=\frac{31}{150}=0.207$ estimated proportion of boy overweigth

p_o=0.15 is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)

1) Concepts and formulas to use

We need to conduct a hypothesis in order to test the true proportion of boys obese is higher than 0.15.:

Null hypothesis: $p \leq 0.15$

Alternative hypothesis: p 0.15

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

2) The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value p_o .

3) Decision rule

For this case we need a value on the normal standard distribution who accumulates 0.05 of the area on the right tail and on this case this value is:

$z_{crit}= 1.64$

And the rejection zone would be z1.64

4) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.207 -0.15}{\sqrt{\frac{0.15(1-0.15)}{150}}}=1.955$

5) Statistical decision

Answer from: Quest

-1/2 +2

step-by-step explanation:

Answer from: Quest

The difference is 5,100m?

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In a recent study, researchers found that 31 out of 150 boys aged 7-13 were overweight or obese. On...