A CI is desired for the true average stray-load loss (watts) for a certain type

Question

A CI is desired for the true average stray-load loss (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 = 2.8. (Round your answers to two decimal places.) (a) Compute a 95% CI for when n = 25 and x = 53.7. (b) Compute a 95% CI for when n = 100 and x = 53.7. (c) Compute a 99% CI for when n = 100 and x = 53.7. (d) Compute an 82% CI for when n = 100 and x = 53.7. (e) How large must n be if the width of the 99% interval for is to be 1.0? (Round your answer up to the nearest whole number.)

Explanation / Answer

a) here std error =std deviaiton/(n)1/2 =2.8/(25)1/2 =0.56

for 95% CI ; critical value of z=1.96

therefore 95% CI for =sample mean -/+ z*Std error =52.6024 ; 547976

b)

std error =std deviaiton/(n)1/2 =2.8/(100)1/2 =0.28

for 95% CI ; critical value of z=1.96

therefore 95% CI for =sample mean -/+ z*Std error =53.1512 ; 54.2488

c)

for 99% CI ; critical value of z=2.5758

therefore 95% CI for =sample mean -/+ z*Std error =52.9788 ; 54.4212

d)

for 82% CI ; critical value of z=1.3408

therefore 95% CI for =sample mean -/+ z*Std error =53.3246 ; 54.0754

e)

for 99% CI ; z =2.5758

margin of error E =width/2 =0.5

sample size n=(z*/E)2 =~209

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