STAT101 Worksheet:Hypothesis Testing

For the following examples:

  • Make a list of “Given” information
  • Write the null and alternative hypotheses in both statistical form and words.
  • Identify the claim
  • Draw a picture
  • Find the critical values and critical regions
  • Determine the test statistic
  • Decide whether to reject or retain the null hypothesis
  • Interpret the decision in terms of the original data.

1)A coffee shop claims that its fresh-brewed drinks have a mean caffeine content of 80 milligrams per 5 ounces. You work for a health agency and are asked to test this claim. You find that a random sample of 42 five-ounce servings has a mean caffeine content of 83 milligrams and a standard deviation of 35 milligrams. At the  = .05 level of significance do you have enough evidence to reject the shop’s claim?

2)In your work for a national health organization, you are asked to monitor the amount of sodium in a certain brand of cereal. You find that a random sample of 52 cereal servings has a mean sodium content of 232 milligrams with a standard deviation of 10 milligrams. At  = .04, can you conclude that the mean sodium content per serving of cereal is less than 230 milligrams?

3)The average U.S. wedding includes 125 guests. A random sample of 35 weddings during the past year in a particular city had a mean of 110 guests and a standard deviation of 30. Is there sufficient evidence at the  = .01 level of significance that the number of guests differs from the national average?

4)As part of your work for an environmental awareness group, you want to test the claim that the mean waste generated by adults in the United States is more than 4 pounds per day. In a random sample of ten adults, you find the mean waste generated per day is 4.3 pounds with a standard deviation of 1.2 pounds. At the  = .05 level of significance, can you support the claim?

5)An environmentalist estimates that the mean waste recycled by adults in the United States is more than 1 pound per day. You want to test this claim. You find that the mean waste recycled per person per day for a random sample of 12 adults is 1.2 pounds with a standard deviation of .3 pounds. At the  = .05 level of significance, can you support the claim?