Question

1. Childhood obesity: A national healthy survey weighed a sampled of 546 boys aged 6-11 and found that 74 of them were overweight. They weighed a sample of 455 girls aged 6-11 and found that 75 of them were overweight. Can you conclude that the proportion of boys who are overweight is less than the proportion of girls who are overweight? Use the α =0.10 level of significance

1. State the null and alternative hypothesis

2. Compute the p-value and Testing Value

3. Do you reject the null hypothesis? Explain?

4. Can you conclude that the proportion of boys who are overweight is less than the proportion of girls who are overweight

Answer 1

Here, we have given that,

n1= number of healthy boys aged 6-11 = 546

x1= number of healthy boys aged 6-11 found that they were overweight=74

=Sample proportion of healthy boys aged 6-11 found that they were overweight

=

n2= number of healthy girls aged 6-11 = 455

x2= number of healthy girls aged 6-11 found that they were overweight=75

=Sample proportion of healthy girls aged 6-11 found that they were overweight

=

Claim: To check whether the population proportion of healthy boys aged 6-11 found that they were overweight is less than the population proportion of healthy girls aged 6-11 found that they were overweight.

The null and alternative hypotheses are as follows:

Versus

Where p1 = The population proportion of healthy boys aged 6-11 found that they were overweight.

p2= The population proportion of healthy girls aged 6-11 found that they were overweight.

This is the left one-tailed test.

Here, we are using the two-sample proportion test.

Now, we can find the test statistics

Z-statistics=

                 =

       =

= -1.29

The test statistics is -1.29.

Now, we can find the p-value

P-value =P( Z <  -1.29) as this is left one tailed test

              =  0.0985 Using standard normal z table see the value corresponding to the z=-1.29

we get the p-value is 0.0985

Decision:

= level of significance= 0.10

Here, P-value (0.0985) less than (>)  0.10

Conclusion:

we reject the Null hypothesis Ho

we conclude that there is sufficient evidence to support the claim the population proportion of healthy boys aged 6-11 found that they were overweight is less than the population proportion of healthy girls aged 6-11 found that they were overweight.i.e. .