A 95% confidence interval on the difference in two means 3 lessthanorequalto mu_

Question

A 95% confidence interval on the difference in two means 3 lessthanorequalto mu_1 - mu_2 lessthanorequalto 5. Which of the following statements is false? The null hypothesis in H_0: mu_1 = mu_2 versus H_1: mu_1 notequal m_2 is not rejected at the 5% level of significance. A 99% confidence interval would be longer. If the sample sizes had been larger, the 95% confidence interval would have been shorter. The null hypothesis in H_0: mu_1 - mu_2 = 4 versus H_1:mu_1 - mu_2 notequal 4 is not rejected at the 5% level of significance.

Explanation / Answer

Since 3<= U1-U2 <=5 , Hence by using the given information we can say that the first option is false.

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