One population CI with unknown standard deviation
Assume you are the manager of a mustard seed factory in Colombia. Your company has received complaints that there is not enough mustard seed in your economy size packages.
You ask your supervisor and chief operating officer Juan Valdez to test the new mustard seed packaging machine you are installing. He runs a sample of 36 packages, with the results of package sizes in ounces:
A. Calculate a 95% confidence interval (CI) on the average weight of packaged mustard seed. Explain very carefully to the packaging workers what the 95% confidence interval numbers mean. Include your SPSS output. (1 points)
B. Now, let’s assume that the package claims that it contains 1.7 oz. of mustard seed. Some of the customers claim that there isn’t enough mustard seed in the 1.7 oz. economy size; corporate management is worried that there may be too much. Given the sample of 36, assuming that it is adequate, test the hypothesis that the average amount of mustard seed in the package meets the 1.7 oz. standard with, say, 95% confidence. Be sure to state the null and alternative hypothesis and which you support. Include your SPSS output. (2 points)
Solution: (a) We compute the 95% confidence interval for the population weight of packaged mustard seed with the aid of SPSS.
The 95% CI is (1.7244, 1.8123). This means that there is a 0.95 probability that the real population mean weight is contained by the interval (1.7244, 1.8123).
(b) We have to test the following null and alternative hypotheses:
We use a two-tailed t-test, using SPSS. The output is shown below:
The p-value of the test is p = 0.403, which means that we fail to reject the null hypothesis, at the 0.05 significance level.