Question

Answers to the following questions should be calculated in Matlab and given to 4 decimal places. Be careful not to introduce errors by rounding in any intermediate calculations as this may lead to an incorrect final answer. A confidence interval is desired for the true average load loss μ (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. A random sample of 52 motors were tested and the sample mean load loss was found to be 56.5 and the sample standard deviation was 3.3. (a) Find the standard error of the sample mean, x¯. __________ (b) State the degrees of freedom. ____________ (c) Find the critical value t∗ required for a 95\% confidence interval. __________ (d) Give a 95% confidence interval for μ. Enter your answer using the syntax (lower, upper) for example (1.0001, 2.2222). __________

Answer #1

n = 52

x-bar = 56.5

s = 3.3

% = 95

Standard Error, SE = s/√n = 3.3/√52 = 0.457627662

Degrees of freedom = n - 1 = 52 -1 = 51

t- score = 2.007583728

Width of the confidence interval = t * SE = 2.0075837281747 * 0.457627661885814 = 0.918725848

Lower Limit of the confidence interval = x-bar - width = 56.5 - 0.918725847564595 = 55.58127415

Upper Limit of the confidence interval = x-bar + width = 56.5 + 0.918725847564595 = 57.41872585

**ANSWERS:**

(a) 0.4576 (b) 51 (c) 2.0076 (d) [55.5813, 57.4187]

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