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.. Perform a hypothesis test using

alpha equals=0.05 to determine if the proportion of obese individuals without high school diplomas differs from the proportion of obese individuals who have college degrees.? (Note: subscript 1 denotes the population with no high school diplomas and subscript 2 denotes the population with college? degrees.)

No high school diploma	College Degree
x1=67	x2=40
n1=204	n2=182

1. what is the test statistic? round to 3 decimal places

2. Determine the appropriate critical? value(s). round to 3 decimal places

3. Interpret the results

4. Calculate the p-value round to three decimal places

Answer 1

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p₁ : proportion of successes for population 1
p₂ : proportion of successes for population 2
p₁ - p₂ : Difference in proportions
H₀ : p₁ - p₂ = 0
H_A : p₁ - p₂ ? 0

Hypothesis test results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	Z-Stat	P-value
p1 - p2	67	204	40	182	0.10865115	0.045640412	2.3805909	0.0173

Hence,

1. Test statistic = 2.381

2. Critical values at 0.05 level of significance = -1.96, 1.96

3. Reject Ho because test statistic is greater than the upper critical value. We have sufficient evidence to conclude that the proportion of obese individuals without high school diplomas differs from the proportion of obese individuals who have college degrees.

4. p - Value = 0.017