Question

A random sample of 100 students at a high school was asked whether they would ask their father or mother for help with a homework assignment in science. A second sample of 100 different students was asked the same question in history. If 46 students in the first sample and 47 students in the second sample replied that they turned to their mother rather than their father for help, test the claim whether the difference between the proportions is due to chance. Use α = 0.02. Identify the claim, state the null and alternative hypotheses, find the critical value, find the standardized test statistic, make a decision on the null hypothesis (you may use a P-Value instead of the standardized test statistic), write an interpretation statement on the decision.

Answer 1

Let p1 be the population proportion for the first sample and p2 be the population proportion for the second sample .

For the first sample : n1=100 , X1=46

For the second sample : n2=100 , X2=47

The sample proportions are given by ,

The pooled estimate is ,

a) Claim :

b) The null hypothesis is ,

The alternative hypothesis is ,

c) The critical values are ,  

Rejection region :

d) The standardized test statistic is ,

e) Decision : Here , the value of the test statistic is does not fall in the rejection region.

Therefore , fail to reject the null hypothesis.

f) Interpretation : Hence , there is not sufficient evidence to support the claim that there is difference between the proportions is due to chance.

P-value =

; From the standard normal probability table

Here , p-value =0.8886>

Therefore , fail to reject the null hypothesis.