A USA Today/Gallup poll asked a group of unemployed and underemployed Americans if they have had major problems in their relationships with

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

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Adeline 6 days 2021-10-08T07:24:15+00:00 2 Answers 0

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    0
    2021-10-08T07:25:58+00:00

    Answer:

    Null hypothesis: H₀: p₁ = p.

    Alternate hypothesis: H₀: p₁ ≠ p.

    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 p= the proportion of unemployed people who had relationship problems and p= 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 = p.

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

    0
    2021-10-08T07:26:07+00:00

    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.

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