Question

A USA Today/Gallup poll 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

Answer 1

Answer:

Null Hypothesis, $H_0$ : $p_1=p_2$

Alternate Hypothesis, $H_1$ : $p_1\neq p_2$

Step-by-step explanation:

We are given that A USA Today/Gallup poll 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).

Also, 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.

Now, let $p_1$ = proportion of unemployed Americans who had major problems in relationships as a result of their employment status.

and $p_2$ = proportion of underemployed Americans who had major problems in relationships as a result of their employment status.

Now, the hypotheses for evaluating if the proportions of unemployed and underemployed people who had relationship problems were different is given by;

Null Hypothesis, $H_0$ : $p_1=p_2$ {means proportions of unemployed and underemployed people who had relationship problems are same}

Alternate Hypothesis, $H_1$ : $p_1\neq p_2$ {means proportions of unemployed and underemployed people who had relationship problems were different}

And for testing we will z-test with corresponding test statistics.

Answer 2

Answer:

Null hypothesis: H₀: p₁ = p₂.

Alternate hypothesis: H₀: p₁ ≠ p₂.

Step-by-step explanation:

A statistical experiment is conducted to determine whether the proportions of unemployed and underemployed people who had relationship problems were different.

Let p₁ = the proportion of unemployed people who had relationship problems and p₂ = the proportion of underemployed people who had relationship problems.

A hypothesis test for difference between proportions, can be conducted to determine if there is any difference between the two population proportions.

Use a z-test for the test statistic.

The hypothesis test is:

H₀: There is no difference between the proportions of unemployed and underemployed people who had relationship problems, i.e. p₁ = p₂.

Hₐ: There is a significant difference between the proportions of unemployed and underemployed people who had relationship problems, i.e. p₁ ≠ p₂.