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?

• Ho: p_unemployed = p_{underemployed}
  Ha: p_unemployed < p_{underemployed}
• Ho: p_unemployed = p_{underemployed}
  Ha: p_unemployed ≠ p_{underemployed}
• Ho: p_unemployed = p_{underemployed}
  Ha: p_unemployed > p_{underemployed}

(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.

• Since p<α we reject the null hypothesis and accept the alternative
• Since p ≥ α we do not have enough evidence to reject the null hypothesis
• Since p<α we fail to reject the null hypothesis
• Since p ≥ α we accept the null hypothesis
• Since p ≥ α we reject the null hypothesis and accept the alternative

Answer 1

(a)  

Ho: p_unemployed = p_{underemployed}
Ha: p_unemployed ≠ p_{underemployed}

because, here claim whether proportions of unemployed and underemployed people who had relationship problems were different.

hence,  it is a two tailed test.

(b)

Since p ≥ α we do not have enough evidence to reject the null hypothesis

because, rule is

if ( p-Value ) Reject the null hypothesis.

if ( p-Value > ) Failed to reject the null hypothesis.

Here = 0.05 , P-Value = 0.35

here ( p-Value- 0.35 > 0.05)

Hence,

Failed to reject the null hypothesis.

Do not have enough evidence to reject the null hypothesis