Question

People are considered obese when they are approximately 30 pounds over their healthy weight. Two random samples of adults were selected. The individuals in one of the samples lacked high school diplomas. The individuals in the other sample held college degrees. The number of people sampled and the obese individuals from each sample are shown in the accompanying table. Complete parts a and b below. Click the icon to view the obesity data. What are the correct null and alternative hypotheses? B. Ho: P1 – P2 = 0 Hy: P1 - P270 O A. Ho: P1 - P220 H1:21 - P20 O C. Ho: P1 - P2 = 0 H4:21 -P2 > 0 i Obesity and Education What is the test statistic? zo = 2.30 (Round to two decimal places as needed.) No High School Diploma X1 = 71 ny = 207 College Degree X2 = 42 n2 = 178 What is/are the critical value(s)? The critical value(s) is/are . (Round to two decimal places as needed. Use a comma to separate answers as neede Print Done

Answer 1

For No High School Diploma:

n1 = 207, x1 = 71

p̂1 = x1/n1 = 0.343

For College Degree:

n2 = 178, x2 = 42

p̂2 = x2/n2 = 0.236

α = 0.05

Null and Alternative hypothesis:

Ho : p1 - p2 = 0, H1 : p1 - p2 ≠ 0

Pooled proportion:

p̄ = (x1+x2)/(n1+n2) = (71+42)/(207+178) = 0.2935

Test statistic:

z = (p̂1 - p̂2)/√ [p̄*(1-p̄)*(1/n1+1/n2)] = (0.343 - 0.236)/√[0.2935*0.7065*(1/207+1/178)] = 2.30

Critical value :

Two tailed critical value, z crit = NORM.S.INV(0.05/2) = +1.96, -1.96

Reject Ho if z < -1.96 or if z > 1.96

Decision:

p-value < α, Reject the null hypothesis.

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Note: if the significance level, α is different from 0.05 do tell me in comments.