Question

Suppose a consumer group claims that the proportion of households that have 2 working adults is

80%. An employment agency has reason to believe that the proportion differs from 80%. Before the

employment agency starts a big advertising campaign, they conduct a hypothesis test. Their marketing

people survey 150 households with the result that 124 of the households have 2 working adults.

Perform the test at the 10% significance level.

Answer 1

Given that a consumer group claims that the proportion of households that have 2 working adults is 80%, thus population proportion is p = 0.80.

Based on the employment agency belief the hypotheses are:

The marketing people survey N = 150 households with the result that X = 124 of the households have 2 working adults.

Thus the sample proportion is computed as:

Based on the hypothesis it will be a two-tailed test.

Rejection region:

Based on the type of hypothesis and given significance level 0.10 the critical values for the rejection region are calculated using excel formula for normal distribution which is =NORM.S.INV(0.95) thus the Zc is computed as 1.645.

Test Statistic:

P-value:

The P-value based on the Z -score calculated above is computed using excel formula which is =2*(1-NORM.S.DIST(0.816, TRUE)) thus the P-value is computed as 0.4142.

Conclusion:

Since the P-value is greater than 0.10 and Z <Zc hence we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim.