the 95% confidence interval for a parameter µ is (3.1, 5.1) and the 99% confidence interval for µ is (2.8, 5.4). One wants to test the hypotheses H0: µ = 3 v.s. Ha: µ ̸= 3. a. Will H0: µ = 3 be rejected at significance level α = 0.05? Why or why not?

Suppose you are testing the hypotheses  H0:μ=10 and Ha:μ≠10, and the p−value is 0.06. Would a 90% confidence interval for μ include the value 10? Answer choices: No. A p−valuep−value of 0.06 indicates that the results observed are statistically significant at the 10% level, so the 90% confidence interval will not include 10. No. A p−valuep−value of 0.06 indicates that the results observed are not statistically significant at the 10% level, so the 90% confidence interval will not include 10. Yes. A p−valuep−value of 0.06 indicates that the results observed are statistically significant at the 10% level, so the 90% confidence interval will include 10. Yes. A p−valuep−value of 0.06 indicates that the results observed are not statistically significant at the 10% level, so the 90% confidence interval will include 10.

d, e and f

The data for a random sample of six paired observations are shown in the table. a. Calculatex and s b. Express μ in terms of μ, and μ₂- c. Form a 90% confidence interval for Hd. d. Test the null hypothesis Ho: H = 0 against the alternative hypothesis H₂: #0. Use α=0.10. a. Calculate the difference between each pair of observations by subtracting observation from observation 1. Find X- (Round to two decimal places as needed.) (-) Pair 1 2 5 6 Population 1 Sample (Observation 1) 5 12 11 6 3 3 Population 2 Sample (Observation 2) 3 Q