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

Question

A CI 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 sigma = 2.9. (Round your answers to two decimal places.) (a) Compute a 95% CI for mu when n = 25 and bar x = 54.5. watts (b) Compute a 95% CI for mu when n = 100 and bar x = 54.5. watts (c) Compute a 99% CI for mu when n = 100 and bar x = 54.5. watts (d) Compute an 82% CI for mu when n = 100 and bar x = 54.5. watts (e) 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 =

Explanation / Answer

(a) for small sample size n<30 we use t-value as given for calculation of confidence interval .

(1-alpha)*100% confidence interval for population mean=sample mean±t(alpha/2,n-1)*sd/sqrt(n)

here n=25

95% confidence interval for population mean=mean±t(0.05/2, 25-1)*sd/sqrt(n)=54.5±2.06*2.09/sqrt(25)

=54.5±0.86=(53.64,55.36)

(b) if n>30 we use z-value for calculation of confidence interval.

(1-alpha)*100% confidence interval for population mean=sample mean± z(alpha/2)*sd/sqrt(n)

95% confidence interval for mean=54.5±z(0.05/2)*2.09/sqrt(100)=54.5±1.96*2.09/sqrt(100)=54.5±0.41=(54.09,54.91)

(c) if n>30 we use z-value for calculation of confidence interval.

(1-alpha)*100% confidence interval for population mean=sample mean± z(alpha/2)*sd/sqrt(n)

99% confidence interval for mean=54.5±z(0.01/2)*2.09/sqrt(100)=54.5±2.58*2.09/sqrt(100)=54.5±0.54=(53.96,55.04)

(d) 82% confidence interval for mean=54.5±z(0.18/2)*2.09/sqrt(100)=54.5±1.34*2.09/sqrt(100)=54.5±0.28=(54.22,54.78)

(e)width of (1-alpha)*100% confidence=z(alpha/2)*sd/sqrt(n)

width of 99% confidence=z(0.01/2)*2.09/sqrt(n)

or, 1=2.58*2.09/sqrt(n)

or, sqrt(n)=5.3922

or,n=29.08 ( next whole number is 30)

so answer is 30.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.