Question 21 In a random sample of 40 refrigerators the mean

Question 21)

In a random sample of 40 refrigerators, the mean repair cost was $131.00 and the population standard deviation is $19.40. A 90% confidence interval for the population mean repair cost is (125.95,136.05). Change the sample size to n = 80. Construct a 90% confidence interval for the population mean repair cost. Which confidence interval is wider? Explain. Construct a 90% confidence interval for the population mean repair cost. The 90% confidence interval is (Round to two decimal places as needed.) Which confidence interval is wider? Explain. Choose the correct answer below. A. The n = 80 confidence interval is wider because a larger sample is taken, giving more information about the population. B. The n = 40 confidence interval is wider because a smaller sample is taken, giving less information about the population. C. The two intervals are the same size because the confidence interval is based on the level of confidence and sample standard deviation.

Solution

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.05          
X = sample mean =    131          
z(alpha/2) = critical z for the confidence interval =    1.644853627          
s = sample standard deviation =    19.4          
n = sample size =    80          
              
Thus,              
              
Lower bound =    127.4323356          
Upper bound =    134.5676644          
              
Thus, the confidence interval is              
              
(   127.4323356   ,   134.5676644   ) [ANSWER]

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The n = 40 confidence interval is wider because a smaller sample is taken, giving les information about the population. [OPTION B]