Question

The random sample shown below was selected from a normal distribution. 8​, 9​, 6​, 5​, 5​, 3 Complete parts a and b. a. Construct a 99​% confidence interval for the population mean mu. left parenthesis nothing comma nothing right parenthesis ​(Round to two decimal places as​ needed.) b. Assume that sample mean x overbar and sample standard deviation s remain exactly the same as those you just calculated but that are based on a sample of nequals25 observations. Repeat part a. What is the effect of increasing the sample size on the width of the confidence​ intervals? The confidence interval is left parenthesis nothing comma nothing right parenthesis . ​(Round to two decimal places as​ needed.) What is the effect of the sample size on the width of the confidence​ interval? A. As the sample size​ increases, the width increases. B. As the sample size​ increases, the width decreases. C. As the sample size​ increases, the width stays the same.

Answer 1

	x	(x-xbar)^2
	8	4
	9	9
	6	0
	5	1
	5	1
	3	9
Sum	36	24

Mean(x)=xbar=sum(x)/n	6
standard deviation(s)=sum(x-xbar)^2/n-1	2.19089
n	6

for 99 % confidence level with degree of freedom (n-1)=5
c	0.01
degrres of freedom	5
t=critical value obtain using t-table with corresponding df=n-1	4.032143
Margin of error =t*s/sqrt(n)	3.606458
LCL=xbar-ME	2.393542
UCL=xbar+ME	9.606458

#99 ​% confidence interval for the population mean =(2.39 ; 9.61)

Ansb:

n=25

xbar=6

#sample standard devaition=s=2.19

# s/sqrt(n)=2.19/sqrt(25)=0.4382

for 99 % confidence level with degree of freedom (n-1)=24
c	0.01
degrres of freedom	24
t=critical value obtain using t-table with corresponding df=n-1	2.796939
Margin of error =t*s/sqrt(n)	1.225557
LCL=xbar-ME	4.774443
UCL=xbar+ME	7.225557

#99 ​% confidence interval for the population mean =(4.77 ; 7.23)

#What is the effect of the sample size on the width of the confidence​ interval?

as we increase the sample size ; confidence interval width reduces

B. As the sample size​ increases, the width decreases.

#Option B is correct