Question

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 packages to contain a mean of 8.17 ounces so that the probability of producing a package that contains less than 8 ounces is very small. A sample of 50 packages is selected periodically and weighed, and the packaging process is stopped if there is evidence that the mean packaged amount is statistically different than 8.17 ounces. (They don’t want to under-fill or over-fill.) Suppose that a particular sample of 50 packages had a mean weight of 8.159 ounces, with a sample standard deviation of 0.051 ounces.

a. Use the appropriate hypothesis test to determine if there is evidence that the population mean is different from 8.17 ounces (use a 0.05 level of significance). Determine the p-value and interpret its meaning

b. Construct a 95% confidence interval of the mean population weight and interpret its meaning.

c. Based on the information in (a) and (b), what is your decision as process manager?

Answer #1

To Test :-

H0 :-

H1 :-

Test Statistic :-

t = -1.5251

Test Criteria :-

Reject null hypothesis if

Result :- Fail to reject null hypothesis

Decision based on P value

P - value = P ( t > 1.5251 ) = 0.1337

Reject null hypothesis if P value <
level of significance

P - value = 0.1337 > 0.05 ,hence we fail to reject null
hypothesis

Conclusion :- Fail to reject null hypothesis

There is insufficient evidence to support the claim that that the population mean is different from 8.17 ounces at 5% level of significance.

Part b)

Confidence Interval

Lower Limit =

Lower Limit = 8.1445

Upper Limit =

Upper Limit = 8.1735

95% Confidence interval is ( 8.1445 , 8.1735 )

Since lies in the interval, hence we Fail to reject null hypothesis at 5% level of significance.\

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