) In 2005, the Health Department in Marion County, Indiana measured the heights and weights of 90,147 school-age children, allowing exact determination of their BMIs. Among the chil-dren participating in the study, 22% were considered obese. Does this indicate that the true obesity rate for children in Marion County is different from the national average

Since the calculated z=40  falls in the critical region this indicates that the true obesity rate for children in Marion County is different from the national average at the 0.05 significance level. We reject the null hypothesis that population proportion is 0.17.

Step-by-step explanation:

The national average is 17% .The z proportional hypothesis test is used.

1) Let the null and alternate hypothesis be

H0: p =0.17

against the claim

Ha: p ≠ 0.17

Choose the significance level ∝= 0.05

The critical region is z > 1.96  and Z <- 1.96 because  it is two tailed test.

Computing

z= p^-p / sqrt [pq/n]

Z= 0.22-0.17/ √0.17*(1- 0.17)/90147

z= 39.965

Since the calculated z=40  falls in the critical region this indicates that the true obesity rate for children in Marion County is different from the national average at the 0.05 significance level. We reject the null hypothesis that population proportion is 0.17.

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