Question

Dole Pineapple Inc. is concerned that the 16-ounce can of sliced pineapple is being overfilled. Assume the population standard deviation of the process is .04 ounce. The quality control department took a random sample of 60 cans and found that the arithmetic mean weight was 16.05 ounces. At the 3% level of significance (Step 2), can we conclude that the mean weight is greater than 16 ounces?

Step 1: State the null hypothesis (H0) and the alternate hypothesis (H1). (insert >, >, =,< or <) where appropriate. Ho:  ______ 16 H1:  _______16

Step 2: you select the level of significance, =.03 (Given in problem description)

Step 3: Identify the test statistic (circle ‘t distribution’ or ‘Normal Curve (z)’) use the t distribution or Normal Curve (z)

Step 4: Formulate the decision rule Reject Ho if _______________________

Step 5: Take a sample arrive at a decision

Step 6: Interpret the results (circle ‘Reject’ or ‘Accept’) circle ‘are’ or ‘are not’) Reject or Accept Ho. The cans are or are not being overfilled.

Please show legible work!

Answer 1

a. Here claim is that the mean weight is greater than 16 ounces.

So hypothesis is vs

b. Here

So level of significance is 0.03

c. As population standard deviation of the process is .04 ounce, so we will use z distribution

So

d. The z-critical value for a right-tailed test, for a significance level of α=0.03 is

zc​=1.88

Graphically

If zstat>zcritical=1.88, we Reject the null hypothesis

Step 5: As zstat>zcritical we reject the null hypothesis

Step 6: We reject the null hypothesis, which means we have sufficient evidence to support the claim that mean is greater than 16

Hence cans are being overfilled.