Stats

Chapter 9 and 10 Activity This activity contains 2 confidence interval problems and 2 sample size problems from Chapter 9, along with 4 hypothesis tests from Chapter 10.

For confidence intervals, present your results in a sentence.

For each hypothesis test use the standard 5-step procedure. Two of the tests will fail their conditions, forcing you to use the alternative test:

• one-proportion (binomial) • one-mean (sign test)

1) Here are 10 randomly selected blood sugar levels from a laboratory. (Levels measured after a 12-hour fast in mg/DL.)

105 89 96 135 94 91 111 107 141 83

Use the data to test the claim that the mean blood sugar level is 100 mg/DL using the 0.05 level of significance.

2) A random sample of 400 college students were asked if they had experienced homelessness at any point in the last year, and 68 said that they had. Construct a 95% confidence interval for the proportion of all college students who have experienced homelessness at some point in the last year.

3) A college administrator wants to estimate the mean credit card debt of students at their school. How large of a sample is required in order to be 95% confident that their estimate is within $200 of the true population mean? The standard deviation of student credit card debt is believed to be approximately $2500.

4) A sample of 35 non-smokers revealed that 31 of them showed traces of a chemical that appears in the blood of people exposed to second-hand smoke. At the 0.05 level of significance test the claim that more than 80% of non-smokers are exposed to second-hand smoke.

5) A magazine article claims that more that 30% of college students own an iPhone. A random sample of 200 college students revealed that 72 of them own an iPhone. Test the magazine’s claim at the 0.05 level of significance.

6) A college administrator wants to estimate what percent of their students get the flu shot. How large of a sample will she need in order to be 90% confident that their estimate is within 4% of the true population proportion?

7) Eight artichoke plants at a farm were selected at random. Here are the number of artichokes produced by each plant last year.

38 32 17 51 40 36 34 39

At the 0.05 level of significance, test the claim that the mean number of artichokes is higher than 30 artichokes.

8) Sixty randomly selected COS students were asked how many units they were enrolled in this semester. The mean for the sample was 14.6 units, with a standard deviation of 4.2 units. Use this sample information to construct a 95% confidence interval for the mean number of units enrolled in by all COS students.