15) The standard deviation of the number of Metropolitan New York Bus Authority
ID: 3133091 • Letter: 1
Question
15) The standard deviation of the number of Metropolitan New York Bus Authority busses that are being repaired on a given day is 6. The Chief Operating Officer takes a sample of 50 days and finds that the mean number of busses being repaired on each day is 82. a) What is a point estimate of the mean number of busses being repaired on each day? b) Construct a 90% CI of the mean number of busses being repaired on each day. c) Construct a 99% CI of the mean number of busses being repaired on each day.
Explanation / Answer
Confidence intervals for population mean
15) The standard deviation of the number of Metropolitan New York Bus Authority busses that are being repaired on a given day is 6. The Chief Operating Officer takes a sample of 50 days and finds that the mean number of busses being repaired on each day is 82.
a) What is a point estimate of the mean number of busses being repaired on each day?
Solution: The point estimate of the mean number of busses being repaired on each day is given as 82.
b) Construct a 90% CI of the mean number of busses being repaired on each day.
Solution: The 90% Confidence interval is given as below:
Confidence Interval Estimate for the Mean
Data
Population Standard Deviation
6
Sample Mean
82
Sample Size
50
Confidence Level
90%
Intermediate Calculations
Standard Error of the Mean
0.8485
Z Value
-1.6449
Interval Half Width
1.3957
Confidence Interval
Interval Lower Limit
80.60
Interval Upper Limit
83.40
c) Construct a 99% CI of the mean number of busses being repaired on each day.
Solution: The 99% confidence interval is given as below:
Confidence Interval Estimate for the Mean
Data
Population Standard Deviation
6
Sample Mean
82
Sample Size
50
Confidence Level
99%
Intermediate Calculations
Standard Error of the Mean
0.8485
Z Value
-2.5758
Interval Half Width
2.1857
Confidence Interval
Interval Lower Limit
79.81
Interval Upper Limit
84.19
Confidence Interval Estimate for the Mean
Data
Population Standard Deviation
6
Sample Mean
82
Sample Size
50
Confidence Level
90%
Intermediate Calculations
Standard Error of the Mean
0.8485
Z Value
-1.6449
Interval Half Width
1.3957
Confidence Interval
Interval Lower Limit
80.60
Interval Upper Limit
83.40
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