A sample of 16 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weights of each bag was then recorded. The mean weight was two ounces with a standard deviation of 0.12 ounces. The population standard deviation is known to be 0.1 ounce.Construct a 90% confidence interval for the population mean weight of the candies.What is the error bound? (Round to three decimal places)

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Asked Nov 16, 2019
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A sample of 16 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weights of each bag was then recorded. The mean weight was two ounces with a standard deviation of 0.12 ounces. The population standard deviation is known to be 0.1 ounce.

Construct a 90% confidence interval for the population mean weight of the candies.

What is the error bound? (Round to three decimal places)

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Expert Answer

Step 1

Given information is below,

Sample size (n) = 16,

Mean (μ) = 2 ounces,

Population standard deviation (σ) = 0.1 ounce.

Step 2

Formula for confidence interval for population mean is,

CI Z
for 90% confidence, z-value is 1.645
here
error bound (E) = Z
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CI Z for 90% confidence, z-value is 1.645 here error bound (E) = Z

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Step 3

Now, substitute given values...

0.1
21.645
/16
2+0.041125
CI-(1.958875, 2.041125)
CI (1.96, 2.04) for 2 decimal places
CI 1.96 u<2.04
이들
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0.1 21.645 /16 2+0.041125 CI-(1.958875, 2.041125) CI (1.96, 2.04) for 2 decimal places CI 1.96 u<2.04 이들

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