Assume we have an i.i.d. sample from a normal distribution with standard deviation 9. There are n = 25 observations in total and the sum of the observations is 1807.5. We wish to test
H0: µ = 75 vs. HA: µ ≠ 75 at significance level α0 = 0.01.
i) What is the criterion you would use to reject the null hypothesis, H0, in favor of the alternative hypothesis, HA? Write this out explicitly. – 4 pts
ii) Using the criterion in part (i), what conclusion would one draw based on the above information; accept the null hypothesis or reject it? – 2 pts
iii) what kind of error could have been made?

Question

Assume we have an i.i.d. sample from a normal distribution with standard deviation 9.  There are n = 25 observations in total and the sum of the observations is 1807.5.  We wish to test 
H0: µ = 75	vs.	HA: µ ≠ 75 	at significance level α0 = 0.01.
i)	What is the criterion you would use to reject the null hypothesis, H0, in favor of the alternative hypothesis, HA?  Write this out explicitly. – 4 pts
ii)	Using the criterion in part (i), what conclusion would one draw based on the above information; accept the null hypothesis or reject it? – 2 pts
iii) what kind of error could have been made?

zarkon · Answer

you need to calculate $Z$ and $Z_{\alpha/2}$

reject $H_0$ when $|Z|>Z_{\alpha/2}$

anonymous · Answer

how would you do that

anonymous · Answer

standardize your z first:by subtracting the sample mean by the pop mean then divide by std dev. Now compare your calculated z with the the corresponding Z(significance level)using your chart (if your using excel, then use Inverse student-t).  if it is more than the positive Z(alpha) or less than the negative, your looking at rejecting H(Knot).

^^its not  very technical but I hope it helps

zarkon · Answer

I assume that the 9 is the population standard deviation.  If that is the case we do not need the t-distribution.

anonymous · Answer

sample size is less than 30 no ?

zarkon · Answer

he is sampling from a normal distribution...so that doesn't matter