A 95% confidence interval for X Y is (-0.3, 0.15). Based upon the data from whic

Question

A 95% confidence interval for X Y is (-0.3, 0.15). Based upon the data from which the confidence interval was constructed, someone wants to test H0: X = Y versus HA : X = Y at the = 5% significance level.

(a) Based upon the confidence interval, what is your conclusion of the hypothesis test? (Explain)

(b) Can we use the above confidence interval to conduct the hypothesis test at the = 2% level? Why or why not?

(c) Can we use the above confidence interval to conduct the hypothesis test at the = 10% level? Why or why not?

(d) TRUE or FALSE, the probability that X Y is contained within (-0.3, 0.15) is 95%. Explain.

Explanation / Answer

Ans:

a)CI interval for X Y is (-0.3, 0.15)

As,the above confidence interval includes 0,so we can conclude that there is no difference in means(or both means are equal)

b)98% Confidence interval will be wider than 95% Confidence interval,so it will still include 0,so at = 2% ,we can conclude that there is no difference in means(or both means are equal)

c)90% Confidence interval will be narrower than 95% Confidence interval,so we are not sure whether it will include

0 or not,so we can not use above confidence interval for hypothesis test.

d)True

A 95% confidence interval has a 0.95 probability of containing the population mean.

If repeated samples were taken and the 95% confidence interval computed for each sample, 95% of the intervals would contain the population mean. Naturally, 5% of the intervals would not contain the population mean.

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