Question

A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as eight ounces, the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than eight 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 8.175 ounces, with a sample standard deviation of 0.046 ounce. a. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.10 level of significance.) b. Determine the p-value and interpret its meaning?

Answer 1

Solution :

= 8.17

=8.175

S =0.046

n = 50

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :    = 8.17

H_a :     8.17

Test statistic = t

= ( - ) / S / n

= (8.175-8.17) / 0.046 / 50

= 0.768

Test statistic = t =  0.769

P-value =0.4458

= 0.10

P-value >

0.4458 > 0.10

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that