A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labelled as 8 ounces, the company wants the packages to contain a mean of 8.17 ounce 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 ounce. 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. a. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.05 of significance.) b. Determine the p -value and interpret its meaning.
A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labelled as 8 ounces, the company wants the packages to contain a mean of 8.17 ounce 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 ounce. 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. a. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.05 of significance.) b. Determine the p -value and interpret its meaning.
Solution Summary: The author explains the five-step p-value approach to determine whether the population mean amount is different from 8.17 ounces.
A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labelled as 8 ounces, the company wants the packages to contain a mean of 8.17 ounce 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 ounce. 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.
a. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.05 of significance.)
b. Determine the p-value and interpret its meaning.
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
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