3) A hypothesis test is to be performed to test the equality of two population m

Question

3) A hypothesis test is to be performed to test the equality of two population means. The sample sizes are large and the samples are independent. A 95% confidence interval for the difference between the population means is (1.4, 8.7). If the hypothesis test is based on the same samples, which of the following do you know for sure: A: The hypothesis µ1 = µ2 would be rejected at the 5% level of significance. B: The hypothesis µ1 = µ2 would be rejected at the 10% level of significance. C: The hypothesis µ1 = µ2 would be rejected at the 1% level of significance. 3) A) A and B B) A and C C) A only D) A, B, and C

Explanation / Answer

In statistical test theory, the significance level is the probability of rejecting the null hypothesis when it is true, which is known as Type I error.

The confidence interval at confidence level (1)% for a population statistic contains all the values, when performing hypothesis test against the population statistic, should not be rejected at significance level %.

So if you perform a corresponding hypothesis test while calculating confidence interval, it is correct to say that the significance level is 5% if the confidence level is 95%.

C) A only is the correct option ..

The hypothesis µ1 = µ2 would be rejected at the 5% level of significance

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