Question

Two random samples are taken, one from among first-year students and the other from among fourth-year students at a public university. Both samples are asked if they favor modifying the student Honor Code. A summary of the sample sizes and number of each group answering yes'' are given below: First-Years (Pop. 1):Fourth-Years (Pop. 2):n1=80,n2=87,x1=35x2=48 Is there evidence, at an α=0.03 level of significance, to conclude that there is a difference in proportions between first-years and fourth-years? Carry out an appropriate hypothesis test, filling in the information requested (to at least three decimal places, without rounding in intermediate steps). Remember that for the test of equality of two proportions, the SE requires the use of the pooled proportion. A. The value of the standardized test statistic: B. The p-value is

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	35	80	48	87	-0.11422414	0.077449003	-1.4748303	0.1403

Hence,

A) Standardized test statistic = -1.4748

B) p - Value = 0.1403

Do not reject Ho