Question

If in a two-tailed, two-sample test of proportions for independent samples, we fail to reject the...

If in a two-tailed, two-sample test of proportions for independent samples, we fail to reject the null hypotheses, then we can conclude that

Multiple Choice

  • a difference exists between the population proportions.

  • we have no evidence that a difference exists between the population proportions.

  • the difference between sample proportions is definitely zero.

  • the difference between the population proportions is 1.

Math   Statistics-And-Probability   
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Answer #1

The correct answer is (2), i.e., "We have no evidence that a difference exists between the population proportions."

When we are performing a two-tailed hypothesis with a given significance level of and based on the test-statistic, if we Fail to reject the null hypothesis, then we conclude that- "At significance level of the sample data does not provide sufficient evidence to support the alternative hypothesis." As in context of this question, we conclude that, there is insufficient evidence to reject the null hypothesis.

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