A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the pack-ages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.159 ounces, with a sample standard deviation of 0.051 ounce. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.05 level of significance.)Determine the p- value and interpret its meaning.

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Asked Nov 17, 2019
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A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the pack-ages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.159 ounces, with a sample standard deviation of 0.051 ounce.

 

  1. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.05 level of significance.)
  2. Determine the p- value and interpret its meaning.
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Expert Answer

Step 1

It is given that sample mean and standard deviation are 8.159 and 0.051, respectively.

The test hypotheses are:

Null hypothesis:

H0: μ = 8.17.

Alternative hypothesis:

H1: μ ≠ 8.17.

Step 2

As the population standard deviation is unknown, the sample standard deviation must be used while performing the test. Thus, the suitable test to use ...

х — и
n
8.159 8.17
0.051
50
=-1.528
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х — и n 8.159 8.17 0.051 50 =-1.528

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