Question

Dole Pineapple Inc. is concerned that the 462 mL can of sliced pineapple is being overfilled. The population standard deviation is 0.87 mL. The quality control department took a random sample of 50 cans and found that the arithmetic mean volume was 463.4 mL.

At the 0.10 level of significance, can we conclude that the mean volume is greater than 462 mL?

a. What is the decision rule? (Round the final answer to 3 decimal places.)

Reject H₀: μ ≤ 462 and accept H₁: μ > 462 when the test statistic is  (Click to select)  equal to  less than  greater than     .

b. What is the value of the test statistic? (Round the final answer to 2 decimal places.)

Value of the test statistic =            

c. What is your decision regarding H₀?

There is  (Click to select)  not enough  enough  evidence to conclude that the cans are being overfilled.

d. What is the p-value?

The p-value is  

Answer 1

Given : Sample size=n=50

Sample mean=463.4

Population standard deviation=0.87

Significance level=0.10

Hypothesized value=462

Hypothesis: Vs  

a. The critical value is ,

; From Z-table

Decision rule : Rejecy Ho if Z>1.28

The test statistic is ,

c) Decision : Here , Z-stat=11.38>1.28

Therefore , reject Ho.

There is enough evidence to conclude that the cans are being overfilled.

d) The p-value is ,

p-value=

The Excel function is , =1-NORMDIST(11.38,0,1,TRUE)