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Math Help - P-value rejecting alt hypothesis when it shouldn't

  1. #1
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    P-value rejecting alt hypothesis when it shouldn't

    -------------Belief in Afterlife
    Gender------Yes---No---Total
    Female------509---116---625
    Male--------398---104---502


    Test the claim that the proportion of females who believe in an afterlife is larger than the proportion of males.

    Null Hypothesis= Ho: p1=p2
    Alternative Hypothesis= Ho: p1>p2

    My z score was 0.9080619
    My p-value was 0.1819
    The significance level was 0.05

    Now here is my problem, since the p-value is greater then the significance level then I would fail to reject aka accept the null hypothesis and reject the alternative hypothesis. This means that the proportion of women who believe in the afterlife is NOT greater then men who do. HOWEVER by doing simple calculations from the data table above the proportion of women is .81 where is the proportion of men is .79. Why would my p-value say something that isn't true in the first place?

    and no my p-value is correct as well as my z-score according to my statcrunch computer program.
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  2. #2
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    Quote Originally Posted by statnoob View Post
    -------------Belief in Afterlife
    Gender------Yes---No---Total
    Female------509---116---625
    Male--------398---104---502


    Test the claim that the proportion of females who believe in an afterlife is larger than the proportion of males.

    Null Hypothesis= Ho: p1=p2
    Alternative Hypothesis= Ho: p1>p2

    My z score was 0.9080619
    My p-value was 0.1819
    The significance level was 0.05

    Now here is my problem, since the p-value is greater then the significance level then I would fail to reject aka accept the null hypothesis and reject the alternative hypothesis. This means that the proportion of women who believe in the afterlife is NOT greater then men who do. HOWEVER by doing simple calculations from the data table above the proportion of women is .81 where is the proportion of men is .79. Why would my p-value say something that isn't true in the first place?

    and no my p-value is correct as well as my z-score according to my statcrunch computer program.
    Hi statnnob,

    The statement

    "This means that the proportion of women who believe in the afterlife is NOT greater then men who do."

    is incorrect.

    When a statistical test fails to reject the null hypothesis, this does NOT mean the null hypothesis is true. It just means you do not have adequate data to reject it. If you had more data you might (or might not) be able to reject the null hypothesis. So in your test you do not have sufficient data to show that a greater proportion of women than men believe in the afterlife, but on the other hand you don't have sufficient evidence to show the contrary, either.

    One sometimes hears terminology like "...and therefore we accept the null hypothesis" when a test fails to reject the null hypothesis. This is just sloppy language, and those who use it deserve to be chastised. (Speaking as one who was so chastised by his professor in Stat 101. Ouch.)
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