Unit 9 In-Class Exercise
You are volunteering for a local nonprofit organization whose mission is to improve child literacy. This organization has asked for your help gathering information on the reading activities that local children engage in.
1. For each of the following scenarios, state the null and alternative hypotheses.
Scenario A: You read in a report that preschool-aged children have on average 5.2 books at home. You are concerned that children in your community have fewer books.
Scenario B: The nonprofit recently engaged in a campaign to encourage elementary school children to read more. A previous study found that children in your community read in their free time for 48 minutes per day on average. You would like to find out whether the time spent reading among elementary school students increased after the campaign.
Scenario C: Your local public library reported last year that the average number of children visiting the library each day was 77. You would like to test whether that has changed.
2. Consider Scenario A from the previous question. State whether you made a Type I error, a Type II error, or the correct conclusion.
a. Children in your community have on average less than 5.2 books at home, and you reject the hypothesis that they have greater than or equal to 5.2 books.
b. Children in your community have on average less than 5.2 books at home, and you fail to reject the hypothesis that they have greater than or equal to 5.2 books.
c. Children in your community have on average greater than or equal to 5.2 books at home, and you reject the hypothesis that they have greater than or equal to 5.2 books.
3. What do we call the probability of a Type I error?
4. Now consider Scenario B from the first question. You survey 40 elementary school students on their current reading habits and find that they read 56 minutes per day on average. Assume the standard deviation of reading time per day is 38 minutes. Go through the six steps for testing a hypothesis.
Step 1: (Re)write the null and alternative hypotheses.
Step 2: You choose as the significance level.
Step 3: Calculate the test statistic.
Step 4: Find the critical value(s).
Step 5: Compare the test statistic to the critical value(s).
Step 6: State the conclusion.
5. Why do we say "we fail to reject the null hypothesis" instead of "we accept the null hypothesis"?
6. Now consider Scenario C. You randomly choose 25 days and count the number of children visiting the library on those days. The average for your sample is 63. You also know that the population standard deviation for children visiting the library is 29. Test whether the number of children visiting the library has changed from the previous year using .
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