Question 845:

Asked on March 2, 2010

Tags: 1-sample t-test , 1-sample Z-test

1

Answer:

No answer provided yet.We can use the 1-sample z-test to test the sample mean against the test criteria of 16 ounces. The Null Hypothesis is that the mean weight of the Dole Pineapple cans is equal to or less than 16 ounces. The alternative hypothesis is that the mean weight is greater than 16 ounces. We will reject the Null Hypothesis if the p-value is less than the alpha cut-off value of .05.

The test statistic z, is found as the difference between the sample mean and test mean (16.05-16) = .05ounces. We divide this difference by the standard error of the mean (SE). The SE is found as the standard deviation divided by the square root of the sample size = .03/SQRT(50) = .00424. The test statistic z = .05/.00424 = 11.785.

The one-sided p-value associated with this z-score is well less than .00001 (most z-tables don't go past a z of 6). The p-value can be found by looking up 11.785 in a normal table or using the excel function =NORMSDIST().

Since the p-value is well less than the alpha cutoff of .05 we reject the Null Hypothesis and conclude there is sufficient evidence to say the mean weight is greater than 16 ounces given the sample size of 50.