A simple random sample of size n is drawn from a population

A simple random sample of size n is drawn from a population with x = 59.2 sigma = 3.8 What is the point estimate of the population mean? A significance level of 0.05 is the same as a confidence level of: What is the 90% Cl estimate of the mean if n is 45? What is the 90% Cl estimate of the mean if n is 55? What happens to the confidence interval when n increases? It does not change. It becomes wider. It becomes narrower. It becomes taller.

Solution

2A.

The point estimate of the population mean is the sample mean, x-bar. Thus,

ANSWER: 59.2 [ANSWER, C]

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2B.

significance level = 1 - confidence level

Thus,

significance level = 1 - 0.95 = 0.05 or 5% [ANSWER, B]

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2C.

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 =    59.2          
z(alpha/2) = critical z for the confidence interval =    1.644853627          
s = sample standard deviation =    3.8          
n = sample size =    45          
              
Thus,              
              
Lower bound =    58.26823885          
Upper bound =    60.13176115          
              
Thus, the confidence interval is              
              
(   58.26823885   ,   60.13176115   )

or (58.3, 60.1) [ANSWER, A]

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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 =    59.2          
z(alpha/2) = critical z for the confidence interval =    1.644853627          
s = sample standard deviation =    3.8          
n = sample size =    55          
              
Thus,              
              
Lower bound =    58.35719033          
Upper bound =    60.04280967          
              
Thus, the confidence interval is              
              
(   58.35719033   ,   60.04280967   )

or (58.4, 60.0) [OPTION C]

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2E.

As we can see, it becomes NARROWER. [OPTION C]