An important problem in industry is shipment damage. A pottery producing company

Question

An important problem in industry is shipment damage. A pottery producing company ships its product by truck and determines that it cannot meet its profit expectations if, on average, the number of damaged items per truckload is greater than 11. A random sample of 15 departing truckloads is selected at the delivery point and the average number of damaged items per truckload is calculated to be 11.3 with a calculated sample of variance of 0.64. Select a 90% confidence interval for the true mean of damaged items.

a) [10.68, 11.92]

b) [10.64, 11.36]

c) [53.67, -33.86]

d) [-0.3635, 0.3635]

e) [10.94, 11.66]

f) None of the above

Please explain and show work.

Explanation / Answer

Note that              
Margin of Error E = t(alpha/2) * s / sqrt(n)              
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 =    11.3          
t(alpha/2) = critical t for the confidence interval =    1.761310136          
s = sample standard deviation =    0.8          
n = sample size =    15          
df = n - 1 =    14          
Thus,              
Margin of Error E =    0.363814657          
Lower bound =    10.93618534          
Upper bound =    11.66381466          
              
Thus, the confidence interval is              
              
(   10.93618534   ,   11.66381466   )

Hence,

OPTION E: e) [10.94, 11.66] [ANSWER, E]

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