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**

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