1. A quality control manager wished to estimate the population mean weight of a
ID: 3153309 • Letter: 1
Question
1. A quality control manager wished to estimate the population mean weight of a particular type of coffee can. A sample of 144 cans of coffee yielded a sample mean weight of 16 ounces. The standard deviation of the population is known to be 1.4 ounces.
a. Construct a 95% confidence interval for the mean weight of the population of these cans of coffee. Interpret your interval, and show all work.
2. A local university administers a comprehensive examination to the recipients of a B.S. degree in Business Administration. A sample of 5 examinations is selected at random and scored. The scores are shown below.
Grades: 54 68 75 80 98
a. At 98% confidence, determine a confidence interval for the mean grade of the population. Interpret your results.
Explanation / Answer
1.
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
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 = 0.025
X = sample mean = 16
z(alpha/2) = critical z for the confidence interval = 1.959963985
s = sample standard deviation = 1.4
n = sample size = 144
Thus,
Margin of Error E = 0.228662465
Lower bound = 15.77133754
Upper bound = 16.22866246
Thus, the confidence interval is
( 15.77133754 , 16.22866246 ) [ANSWER]
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Hence, we are 95% confident that the true mean weight of cans of coffee of this type is between 15.77133754 and 16.22866246 ounces. [ANSWER]
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