A container of oil is supposed to contain 1000 milliliters oil. A quality contro

Question

A container of oil is supposed to contain 1000 milliliters oil. A quality control manager wants to be sure that the standard deviation of oil containers is less than 20 milliliters. He randomly selects 10 cans of oil with a mean of 997 milliliters, and a standard deviation of 32 milliliters. Use these sample results to construct a 95% confidence interval for the true value of . Does this confidence interval suggest that the variation in oil containers is at an acceptable level? Show all your work

Explanation / Answer

95% Confidence Interval [974.1, 1019.9] for the true value of the population mean

SMALL SAMPLE, CONFIDENCE INTERVAL, NORMAL POPULATION DISTRIBUTION

x-bar = Sample mean [997]
s = Sample standard deviation [32]
n = Number of samples [10]
df = degrees of freedom [10 - 1 = 9]
For confidence level of 95%, two-sided interval ("look-up" from Table) "t critical value" [2.262]

Resulting Confidence Interval for "true mean":
x-bar +/- (t critical value) * s/SQRT(n) = 997 +/- 2.262 * 32/SQRT(10) = [974.1, 1019.9]


ANSWER:
95% Confidence Interval [974.1, 1019.9] for the true value of the population mean

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