Let\'s examine the relationship between CI\'s and hypothesis tests: (a) You calc

Question

Let's examine the relationship between CI's and hypothesis tests: (a) You calculate a 95% confidence interval for mu and come up with (10, 22). If you test H_0: mu = 27 and use alpha =.05, will you reject H_0? Why or why not? (b) Now you calculate a 95% CI for mu and come up with (-3, 6). If you test H_0: mu = 7 and use alpha = 10, will you reject H_0? Why or why not? (c) Finally, you calculate a 95% CI for for mu and come up with (-34, -28). If you test H_0: mu = -23 and use alpha =.01, will you reject H_0? Why or why not?

Explanation / Answer

a) Reject Ho. (Since Population parameter is outside the given interval)

b) Reject Ho. (Since Population parameter is outside the given interval)

c) Fail to reject Ho. (Since Population parameter is within the given interval)

There is an extremely close relationship between confidence intervals and hypothesis testing. When a 95% (or any % i.e. 90% or 99%) confidence interval is constructed, all values in the interval are considered plausible values for the parameter being estimated. Values outside the interval are rejected as relatively implausible. If the value of the parameter specified by the null hypothesis is contained in the 95% (or any % i.e. 90% or 99%) interval then the null hypothesis cannot be rejected at the 0.05 (0.10 0r 0.01 respectively) level.

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.