We need to find the confidence interval for the SLEEP variable. To do this we ne
ID: 3171376 • Letter: W
Question
We need to find the confidence interval for the SLEEP variable. To do this we need to find the mean and then find the maximum error, rhea we can use a calculator to find the interval, (x - E. x + E) First, find the mean. Under that column. in cell E37. type =AVERAGE (E2:E36) Under that in cell E38. type = STDEV (E2:F36). Now we can find the maximum error the confidence interval. To find the maximum error, we use the "confidence" formula in cell E39. type =CONFIDC.NCEJSORM(0.05, E35, 35) The 0.05 is bawd on the confidence level of 95%. the E38 is the standard deviation and 35 is the member in our sample. You then need to calculate the interval by using a calculator to subtract the maximum error from the mean (x-E) and add it to the mean (x + E)
Explanation / Answer
The data is as follows:-
1. 95% confidence interval
X+-ta/2*S/n
For 34 DF and a=0.025 (0.05/2=0.025 on each side), we get the critical value of t to be 2.0322. Hence, confidence interval would be calculated as below:-
6.6+-2.0322*1.35473/35
LCL=6.6-0.4654=6.1346
UCL=6.6+0.4654=7.0654.
We are 95 % confident that the hours of sleep of the people are between 6.1346 and 7.054.
2. 99% confidence interval
X+-ta/2*S/n
For 34 DF and a=0.005 (0.01/2=0.005 on each side), we get the critical value of t to be 2.7284. Hence, confidence interval would be calculated as below:-
6.6+-2.7284*1.35473/35
LCL=6.6-0.6248=5.9752
UCL=6.6+0.6248=7.2248.
We are 99 % confident that the hours of sleep of the people are between 5.9752 and 7.2248.
X 4 4 4 4 5 5 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 10 Mean 6.6 SD 1.354731. 95% confidence interval
X+-ta/2*S/n
For 34 DF and a=0.025 (0.05/2=0.025 on each side), we get the critical value of t to be 2.0322. Hence, confidence interval would be calculated as below:-
6.6+-2.0322*1.35473/35
LCL=6.6-0.4654=6.1346
UCL=6.6+0.4654=7.0654.
We are 95 % confident that the hours of sleep of the people are between 6.1346 and 7.054.
2. 99% confidence interval
X+-ta/2*S/n
For 34 DF and a=0.005 (0.01/2=0.005 on each side), we get the critical value of t to be 2.7284. Hence, confidence interval would be calculated as below:-
6.6+-2.7284*1.35473/35
LCL=6.6-0.6248=5.9752
UCL=6.6+0.6248=7.2248.
We are 99 % confident that the hours of sleep of the people are between 5.9752 and 7.2248.
As confidence level increases, the range increases. This is because of higher level of confidence.Related Questions
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