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=93,n2=97,x1=62x2=56First-Years (Pop. 1):n1=93,x1=62Fourth-Years (Pop. 2):n2=97,x2=56

Is there evidence, at an ?=0.07?=0.07 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.

A. The value of the standardized test statistic:

Note: For the next part, your answer should use interval notation. An answer of the form (??,a)(??,a) is expressed (-infty, a), an answer of the form (b,?)(b,?) is expressed (b, infty), and an answer of the form (??,a)?(b,?)(??,a)?(b,?) is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. The p-value is:

Answer 1

n1=93

n2=97

here z test for comparing proportion will be used

claim

significance level alpha=0.07 , critical values are -1.8119 and +1.8119

pooled sample proportion is

p= 0.621052

standard error of the test:

SE= 0.070404936

So test statistics will be

z= 1.26904

since this is lower tail test

p value= p(z>1.2690)=0.102212

p-value for two tail =2*0.1022=0.2044

Decision making,

p-value >alpha

0.2044>0.07 ……fail to Reject null hypothesis

We don’t have enough evidence to support the claim that p1 is different from p2.

.................

A) Z test statistics =1.2690

B) (-infty,-1.8119 )U(1.8119, infty).

c) p-value=0.2044

.........................

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