Question

A 95% confidence interval for a population mean is (28, 35). Using the same data at 5% level of significance, what should you decide regarding the hypotheses: = 34 versus ≠ 34 ? A Fail to reject the null hypothesis because 34 falls in the 95% confidence interval. B Fail to reject the null hypothesis because 34 falls outside the 95% confidence interval. C Reject the null hypothesis because 34 falls in the 95% confidence interval. D Reject the null hypothesis because 34 falls outside the 95% confidence interval. E There is not enough information to determine.

Answer 1

Answer:

A) Fail to reject the null hypothesis because 34 falls in the 95% confidence interval.  

Step-by-step explanation:

We are given the following information in the question:

A 95% confidence interval for a population mean is (28, 35)

Alpha, α = 0.05

The null and the alternate hypothesis are:

$H_{0}: \mu = 34\\H_A: \mu \neq 34$

• A confidence interval also known as the acceptance region, is a set of values for the test statistic for which the null hypothesis is accepted.
• If the observed test statistic lies in the confidence interval then we accept the null hypothesis and reject the alternative hypothesis.
• If the observed test statistic is in the critical region then we reject the null hypothesis and accept the alternative hypothesis.

Hence, we fail to reject the null hypothesis and accept it because 34 falls in the 95% confidence interval.