Statistics – Math 1530 Preview for chapter 7 test…Hypothesis Testing!
For all the following problems you should complete a full hypothesis test. Make sure you
include: The original and alternative hypothesis, the test statistic, the critical value, the
traditional method conclusion, and the p-value method conclusion (where appropriate).
1. A company that produces snack foods uses a machine to package 454 grams of pretzels into bags. The net weights
of the bags are normally distributed and the population standard deviation is 7.8 grams. A random sample of 50 bags has a
mean weight of 451 grams. Test the claim that the machine is not filling the bags properly, using a 0.01 significance level.
2. The average retail price for bananas in 1998 was 51 cents per pound as reported by the USDA. A recent sample of
15 markets gave the following prices for bananas in cents per pound. Test the claim that the current mean retail price for
bananas is different from the 1998 mean using a 0.05 significance level.
56 57 50 53 58 57 55 54
57 53 48 51 50 47 55
3. According to the USDA, the proportion of Americans who consume beef on at least a weekly basis is 84%. A
vegetarian group questions this statement and believes that the percentage has lowered recently. A sample study of 82
people resulted in 60 people who ate beef on a weekly basis. Use a 5% significance level to test the claim of the
vegetarian group.
4. A photo chemical is claimed by its manufacturer to have a shelf life that is normally distributed with a mean of
180 days and with a standard deviation of no more than 10 days. Twelve samples were randomly selected and tested with
a standard deviation of 14 days resulting. At the 10% level of significance, test the manufacturer's claim.
5. A poll of 758 adults asked "Do you open presents on Christmas Eve or Christmas Day?" Of those surveyed, 394
said they wait until Christmas Day. At the 5% significance level, test the claim that the majority of adults wait until
Christmas Day to open their presents.
6) It is commonly believed that piglets have a mean weight of 41 pounds with a standard deviation of 9 pounds. Test the
claim that the standard deviation of all piglets in the population is different than 9 pounds using a 5% significance level if
a sample group of 40 had a standard deviation of 11.
