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suppose you are testing Ho:p=.65 versus Ha: p<.65 . for a random sample of 100 people, x=58, where x denotes the number in the sample that have the characteristic of interest . use a .01 level of significance to test this hypothesis.

  • statistics -

    Null hypothesis:
    Ho: p = .65 -->meaning: population proportion is equal to .65
    Alternative hypothesis:
    Ha: p < .65 -->meaning: population proportion is less than .65

    Using a formula for a binomial proportion one-sample z-test with your data included, we have:

    z = (.58 - .65) -->test value (58/100 = .58) minus population value (.65)
    divided by
    √[(.65)(.35)/100] --> .35 represents 1 - .65 and 100 is the sample size.

    Use a z-table to find the critical or cutoff value for a one-tailed test (lower tail) at .01 level of significance. The test is one-tailed because the alternative hypothesis is showing a specific direction (less than).

    If the test statistic exceeds the critical value you find from the table, reject the null. If the test statistic does not exceed the critical value from the table, do not reject the null.

    You can draw your conclusions from there.

    I hope this will help get you started.

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