I need assistance please Chapter is Group Work Math 1240 we find a confidence in

Question

I need assistance please Chapter is Group Work Math 1240 we find a confidence interval for a population mean. Decide if each of these changes would make the confidence wider, narrower, or stay the same. in a) Use a smaller sample. ller standard deviation b) Use a sample with e) Use a sample with a smaller mean but the same standard deviation d) Use a lower confidence level. 4. We are interested in the average score of all golfers on a particular course. Afinar a) We sample 40 golfers at random and find their average score is 92 with standard deviation of 10. Construct a 90% confidence interval for the average score of all golfers on this course. b) Will an 85% confidence interval be wider or narrower? Why? c suppose instead we had sample 60 golfers (instead of only 40) and found the same mean and standard deviation. Will a 90% confidence interval be wider, narrower, or the same as the one we found in part (a)? Why?

Explanation / Answer

3)
a)Wider (As n decreases, margin of error increases , hence confidence interval will become wider)
b)Narrower (As SD decreases, margin of error decreases , hence confidence interval will become narrower)
c)Stay the same (As Mean decreases, margin of error will not change , hence confidence interval will stay the same)
d)Narrower (As z-value decreases, margin of error decreases , hence confidence interval will become narrower)

4)
a)
n=40
SD=10
Mean=92
Confidence = 90%
z-value for 90% = 1.645
Margin of error = (z*SD)/sqrt(n) = (1.645*10)/sqrt(40) = 2.6
Confidence Interval : (92-2.6 , 92+2.6) = (89.4 , 94.6) Answer

b)
85% Confidence Interval will be narrower .(As z-value decreases, margin of error decreases , hence confidence interval will become narrower.)

c)
Confidence Interval will be wider. (As n decreases, margin of error increases , hence confidence interval will become wider).

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