Question

A USA Today/Gallup poll conducted between 2010 and 2011 asked a group of unemployed and underemployed Americans if they have had major problems in their relationships with their spouse or another close family member as a result of not having a job (if unemployed) or not having a full-time job (if underemployed). 27% of the 1,145 unemployed respondents and 25% of the 675 underemployed respondents said they had major problems in relationships as a result of their employment status.

(a) What are the hypotheses for evaluating if the proportions of unemployed and underemployed people who had relationship problems were different?


(b) The p-value for this hypothesis test is approximately 0.35. Explain what this means in context of the hypothesis test and the data.

Answer 1

Explanation:

Given that a USA Today/Gallup poll conducted between 2010 and 2011 asked a group of unemployed and underemployed Americans if they have had major problems in their relationships with their spouse or another close family member as a result of not having a job (if unemployed) or not having a full-time job (if underemployed).

Let p1 be the proportion of I group and p2 for II group.

a) the hypotheses for evaluating if the proportions of unemployed and underemployed people who had relationship problems were different

`H_0: p_1 = p_2\\H_a: p_1 \\eq p_2`

(two tailed test)

b) p value = 0.35

A small p value indicates strong evidence against null hypothesis.

Normally significance level would be 5% or 1% or 10% . If p value is above this value, this proves that null hypothesis can be accepted.

Here p = 0.35 implies that there is no significant different between the two proportions.