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 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 8.152 ounces, with a sample standard deviation of 0.046 ounce.

question 1

Is there evidence that the population mean amount is different from 8.17 ounces( use a 0.10 level of significance)

state the null and alternate hypothesis?

Identify the critical values?

determine the test statistic and state the conclusion?

question 2

determine the p value (round to 4 decimals places) and interpret the meaning?

Choose the correct answer below. A. The​ p-value is the probability of not rejecting the null hypothesis when it is false. B. The​ p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.015 ounce below 8.17 if the null hypothesis is false. C. The​ p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.015 ounce above 8.17 if the null hypothesis is false. D. The​ p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.015 ounce away from 8.17 if the null hypothesis is true.

Answer 1

Step 1

Ho: = 8.17

Ha: 8.17

Step 2: Test statistics

n = 50

sample mean = 8.152

sample sd = 0.046

Assuming that the data is normally distributed and also as the population sd is not given, we will use t stat

t = - 2.767

Step 3

df = 49

= 0.10

t critical (two tailed test) = +/- 1.67655090

p value = 0.0080

As the t stat falls in the rejction area, we reject the Null hypothesis.

Also as the p value is less than , we reject the Null hypothesis.

D. The​ p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.015 ounce away from 8.17 if the null hypothesis is true.