The confidence interval is desired for a true average stray-load loss n (in watt

Question

The confidence interval is desired for a true average stray-load loss n (in watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume the stray-load loss is normally disturbed with sigma = 3.0 a) Compute a two-sided 95% confidence interval for p when n = 25 and is x^bar = 58.3. b) Compute a two-sided 95% confidence interval for p when n = 100 and is x^bar = 58.3. c) How large must n be if the width of the two-sided 99% confidence interval for mu is to be 1.0?

Explanation / Answer

a)

z value at 95% = 1.96

s = 3 . , n = 25 , x = 58.3

CI = mean + / - z * (s / sqrt(n))

= 58.3 + / - 1.96 * (3 / sqrt(25))

= (57.124 , 59.476)

b)

z value at 95% = 1.96

s = 3 . , n = 100 , x = 58.3

CI = mean + / - z * (s / sqrt(n))

= 58.3 + / - 1.96 * (3 / sqrt(100))

= (57.712 , 58.888)

c)

ME = 0.5 , s = 3 , z value = 2.576

ME = z * s / sqrt(n)

0.5 = 2.576 * 3 / sqrt(n)

n = 238.88 = 239

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