Question

Conduct the following test at the a=0.05 level of significance by determining ​(a) the null and alternative​ hypotheses, ​(b) the test​ statistic, and​ (c) the​ P-value. Assume that the samples were obtained independently using simple random sampling.

Test whether p1≠p2. Sample data are x 1 = 28, n 1 = 255, x 2 = 38, and n 2 = 301.

(a) Determine the null and alternative hypotheses. Choose the correct answer below.

A.

Upper H 0 : p 1 equals p 2H0: p1=p2

versus Upper H 1 : p 1 less than p 2H1: p1<p2

B.

Upper H 0 : p 1 equals p 2H0: p1=p2

versus Upper H 1 : p 1 not equals p 2H1: p1≠p2

C.

Upper H 0 : p 1 equals 0H0: p1=0

versus Upper H 1 : p 1 equals 0H1: p1=0

D.

Upper H 0 : p 1 equals p 2H0: p1=p2

versus Upper H 1 : p 1 greater than p 2

b) The test statistic z 0 is ____. ​(Round to two decimal places as​ needed.)

​(c) The​ P-value is _____. ​(Round to three decimal places as​ needed.)

Test the null hypothesis. Choose the correct conclusion below.

A. Reject the null hypothesis because there is not sufficient evidence to conclude that p 1 less than p 2p1<p2.

B. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p 1 not equals p 2p1≠p2.

C.Do not reject the null hypothesis because there is sufficient evidence to conclude that p 1 greater than p 2p1>p2.

D.Reject the null hypothesis because there is sufficient evidence to conclude that p 1 not equals p 2p1≠p2.

Answer 1

p₁: proportion where Sample 1 = Event

p₂: proportion where Sample 2 = Event

Difference: p₁ - p₂

Descriptive Statistics

Sample	N	Event	Sample p
Sample 1	255	28	0.109804
Sample 2	301	38	0.126246

Test

Null hypothesis	H₀: p₁ = p₂
Alternative hypothesis	H₁: p₁ ≠ p₂

Method	Z-Value	P-Value
Normal approximation	-0.60	0.548

Do not reject the null hypothesis because there is not sufficient evidence to conclude that p1≠p2.