A Cl is desired for the true average strayload loss mu watts

A Cl is desired for the true average stray-load loss mu (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with a = 3.1. (Round your answers to two decimal places.) Compute a 95% Cl for,mu when n = 25 and x = 54.7. watts Compute a 95% Cl for mu when n = 100 and x = 54.7. watts Compute a 99% Cl for mu when n = 100 and x = 54.7. watts Compute an 82% Cl for mu when n = 100 and x = 54.7. watts How large must n be if the width of the 99% interval for mu is to be 1.0? (Round your answer up to the nearest whole number.) n = .

Solution

a).

Confidence Interval Estimate for the Mean

Data

Population Standard Deviation

3.1

Sample Mean

54.7

Sample Size

25

Confidence Level

95%

Intermediate Calculations

Standard Error of the Mean

0.6200

Z Value

1.9600

Interval Half Width

1.2152

Confidence Interval

Interval Lower Limit

53.48

Interval Upper Limit

55.92

b).

Confidence Interval Estimate for the Mean

Data

Population Standard Deviation

3.1

Sample Mean

54.7

Sample Size

100

Confidence Level

95%

Intermediate Calculations

Standard Error of the Mean

0.3100

Z Value

1.9600

Interval Half Width

0.6076

Confidence Interval

Interval Lower Limit

54.09

Interval Upper Limit

55.31

c).

Confidence Interval Estimate for the Mean

Data

Population Standard Deviation

3.1

Sample Mean

54.7

Sample Size

100

Confidence Level

99%

Intermediate Calculations

Standard Error of the Mean

0.3100

Z Value

2.576

Interval Half Width

0.7985

Confidence Interval

Interval Lower Limit

53.90

Interval Upper Limit

55.50

d).

Confidence Interval Estimate for the Mean

Data

Population Standard Deviation

3.1

Sample Mean

54.7

Sample Size

100

Confidence Level

82%

Intermediate Calculations

Standard Error of the Mean

0.3100

Z Value

1.3408

Interval Half Width

0.4156

Confidence Interval

Interval Lower Limit

54.28

Interval Upper Limit

55.12

e)

For 99%, z=2.576

d=1

sd=3.1

Sample size = (z²*s²)/d²

= (2.576²*3.1²)/1²

=63.76

The sample size required= 64

Confidence Interval Estimate for the Mean
Data
Population Standard Deviation	3.1
Sample Mean	54.7
Sample Size	25
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	0.6200
Z Value	1.9600
Interval Half Width	1.2152
Confidence Interval
Interval Lower Limit	53.48
Interval Upper Limit	55.92