The manufacturer of a new line of inkjet printers would like

The manufacturer of a new line of ink-jet printers would like to include as part of its advertising the number of pages a user can expect from a print cartridge. A sample of 10 cartridges revealed the following number of pages printed. (Use Student\'s z Distribution Table.) 3,360 2,450 2,550 2,610 2,730 2,610 2,550 3,320 3,390 2,400

a. What is the point estimate of the population mean? (Round your answer to the nearest whole number.) Estimated population mean

b. Develop a 90% confidence interval for the population mean. (Round your answers to 2 decimal places.) Confidence interval for the population mean is between and .

Solution

a)

It is the sample mean,

X = sample mean =    2797   [ANSWER]

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b)      

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.05          
X = sample mean =    2797          
t(alpha/2) = critical t for the confidence interval =    1.833112933          
s = sample standard deviation =    396.7380888          
n = sample size =    10          
df = n - 1 =    9          
Thus,              
              
Lower bound =    2567.018386          
Upper bound =    3026.981614          
              
Thus, the confidence interval is              
              
(   2567.018386   ,   3026.981614   ) [ANSWER]