Please answer them all. A population has sigma = 17.36. A sample of size is take
ID: 3235568 • Letter: P
Question
Please answer them all.
A population has sigma = 17.36. A sample of size is taken from this population with x = 51.45. Find a 98% confidence interval for the population mean. A statement is made that the population mean is between 48.45 and 54.45. With what level of confidence can this statement be made? How large does a sample need to be so that the population mean is known within plusminus 2.5 at a 98% level of confidence? A sample of size 9 is taken from an (approximately normal) population with x = 51.45 and s = 17.36. Find a 98% confidence interval for the population mean. Find 99% upper confidence bound for the population mean.Explanation / Answer
Answer:
1).
Confidence Interval Estimate for the Mean
Data
Population Standard Deviation
17.36
Sample Mean
51.45
Sample Size
100
Confidence Level
98%
Intermediate Calculations
Standard Error of the Mean
1.7360
Z Value
2.33
Interval Half Width
4.0385
Confidence Interval
Interval Lower Limit
47.41
Interval Upper Limit
55.49
2).
Margin of error=54.45-51.45 =3.0
Z=margin of error /se= 1.728=1.73( two decimals)
From z tables we find that confidence level= 92%
3).
Sample Size Determination
Data
Population Standard Deviation
17.36
Sampling Error
2.5
Confidence Level
98%
Intemediate Calculations
Z Value
2.3300
Calculated Sample Size
261.7769
Result
Sample Size Needed
262.0000
4).
Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation
17.36
Sample Mean
51.45
Sample Size
9
Confidence Level
98%
Intermediate Calculations
Standard Error of the Mean
5.786666667
Degrees of Freedom
8
t Value
2.8965
Interval Half Width
16.7608
Confidence Interval
Interval Lower Limit
34.6892
Interval Upper Limit
68.2108
5).
t Value 99% upper
2.8960
Interval Half Width
16.7582
Confidence Interval
Interval Upper Limit
68.2082
Confidence Interval Estimate for the Mean
Data
Population Standard Deviation
17.36
Sample Mean
51.45
Sample Size
100
Confidence Level
98%
Intermediate Calculations
Standard Error of the Mean
1.7360
Z Value
2.33
Interval Half Width
4.0385
Confidence Interval
Interval Lower Limit
47.41
Interval Upper Limit
55.49