A statistics practitioner took a random sample of 47 observations from a populat
ID: 3134376 • Letter: A
Question
A statistics practitioner took a random sample of 47 observations from a population whose standard deviation is 26 and computed the sample mean to be 104. Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits. A. Estimate the population mean with 95% confidence. Confidence Interval = B. Estimate the population mean with 95% confidence, changing the population standard deviation to 40; Confidence Interval = C. Estimate the population mean with 95% confidence, changing the population standard deviation to 6; Confidence Interval =
Explanation / Answer
A statistics practitioner took a random sample of 47 observations from a population whose standard deviation is 26 and computed the sample mean to be 104. Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.
A. Estimate the population mean with 95% confidence. Confidence Interval = (96.57,111.43)
Confidence Interval Estimate for the Mean
Data
Population Standard Deviation
26
Sample Mean
104
Sample Size
47
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
3.7925
Z Value
-1.9600
Interval Half Width
7.4331
Confidence Interval
Interval Lower Limit
96.57
Interval Upper Limit
111.43
B. Estimate the population mean with 95% confidence, changing the population standard deviation to 40; Confidence Interval = (92.56, 115.44)
Confidence Interval Estimate for the Mean
Data
Population Standard Deviation
40
Sample Mean
104
Sample Size
47
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
5.8346
Z Value
-1.9600
Interval Half Width
11.4356
Confidence Interval
Interval Lower Limit
92.56
Interval Upper Limit
115.44
C. Estimate the population mean with 95% confidence, changing the population standard deviation to 6; Confidence Interval =(102.28,105.72)
Confidence Interval Estimate for the Mean
Data
Population Standard Deviation
6
Sample Mean
104
Sample Size
47
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
0.8752
Z Value
-1.9600
Interval Half Width
1.7153
Confidence Interval
Interval Lower Limit
102.28
Interval Upper Limit
105.72
Confidence Interval Estimate for the Mean
Data
Population Standard Deviation
26
Sample Mean
104
Sample Size
47
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
3.7925
Z Value
-1.9600
Interval Half Width
7.4331
Confidence Interval
Interval Lower Limit
96.57
Interval Upper Limit
111.43
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