Answers to the following questions should be calculated in Matlab and given to 4

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 ? (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 46 motors were tested and the sample mean load loss was found to be 58.1 and the sample standard deviation was 3.4 (a) Find the standard error of the sample mean, z (b) State the degrees of freedom |?? (c) Find the critical value t required for a 951% confidence interval (d) Give a 95% confidence interval for ? Enter your answer using the syntax (lower, upper) for example (1.0001, 2.2222)

Explanation / Answer

mean = 58.1 , s = 3.4 , n =46

a)
std. error = s/sqrt(n)
= 3.4/sqrt(46) = 0.50130

b)
degrees of freedom = n -1 = 46 -1 = 45

c)
critical value = +/-2.0141

d)

CI = mean +/- t *(s/sqrt(n))
= 58.1 +/- 2.0141 * (3.4/sqrt(46))
= (57.0903 , 59.1097)

2)
a) p1 = 57/300 = 0.19 , p2 = 50/180 = 0.28
n1 = 300 , n2 = 180

z = ( p1 - p2)/sqrt((p1 ( 1-p1)/n1) +(p2 * (1 -p2)/n2))
= ( 0.19 - 0.28) /sqrt( 0.19 *(1-0.19)/300) + (0.28 * (1 -0.28)/180))
= -2.2271

b) P value = 0.0129

c)
reject the null hypothesis at 0.05 significance level

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