Midterm Exam, Stat 431, Fall 2003
Instructions: This is a semi-closed book exam. Up to three pages of notes are allowed. Show your work and partial
credits will be given. When performing hypothesis tests, clearly state the null and alternative hypotheses and show
the critical value and/or P-value (from the table) where appropriate. Normal, and t tables will be provided.
There are total 30 points distributed as marked. Time = 80 minutes.
1 (8 pts.) In any bottling process a manufacturer will lose money if the bottles contain either more or less
than is claimed on the label. Suppose a quality manager for a catsup company is interested in testing whether the
mean number of ounces per family size bottle differs from the labeled amount of 24 ounces. The manager samples
90 bottles, measures the weight of their contents, and finds that x = 23.96 and s = .32 .
i) Does the sample evidence indicate that the catsup dispensing machine needs adjustment? State null and
alternative hypotheses and test at α = .05.
ii) Find a 99% confidence interval for the mean number of ounces of catsup being dispensed.
iii) Bottles having net weight less than 23.76 ounces are more than 1% underweight, and hence can be cited
by the FDA as being mislabeled. Using the data provided, give the best available estimate of the proportion of
catsup bottles that will fail to meet the FDA standard of weighing at least 23.76 ounces.
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