Practice Quiz III

  1. In a study of human blood types in nonhuman primates, a sample of 71 orangutans were tested and 14 were found to be blood type B. We would like to construct a 95% confidence interval for the relative frequency of blood type B in the orangutan population.
  1. Justify whether you can use the large sample CI or not.
  1. Justify whether you can use the plus four CI.
  1. Compute .
  1. Compute .
  1. Construct a 95% confidence interval for the relative frequency of blood type B in the orangutan population and interpret the results in the problem context.
  1. In populations of the snail Cepaea, the shells of some individuals have dark bands, while other individuals have unbanded shells. Suppose that a biologist is planning a study to estimate the percentage of banded individuals in a certain natural population, and that she wants to estimate the percentage – which she anticipates will be in the neighborhood of 60% - with 95% confidence and a margin of error not to exceed 4 percentage points. How many snails should she plan to collect?

3. An earlier study determined that 60% of women over 50 have annual mammograms. A researcher believes that 60% is no longer valid and that the proportion should be higher. To see if this proportion is still valid he surveys 100 women, 70 of whom say they have annual mammograms.

a. The correct hypotheses for this test are:

b. Justify the assumptions before you compute your test statistic and then compute the test statistic.

c. What is the p-value for this test?

d. What would you conclude from this test at 5% level of significance?

4-5. In the summer of 2003, The New England Journal of Medicine published results of some Scandinavian research. Men diagnosed with prostate cancer were randomly assigned to either undergo surgery or not. Among the 347 men who had surgery (group 1), 16 eventually died of prostate cancer compared with 31 of the 348 men (group 2) who did not have surgery. The researchers want to determine if surgery increases the chance of survival. Let p1: proportion of men that survived after surgery and p2: proportion of men that survived without surgery.
4. Construct a two-tailed 90% confidence interval for the difference between men’s survival without and with surgery and interpret it in terms of the problem context.

a. Justify assumptions for your CI.

b.Compute the 90% confidence interval and interpret it:

5. Apply a Hypothesis testing.

a. What are the null and alternative hypotheses?

b. Justify the assumptions before you compute your test statistic and then compute the test statistic.

These are SRSs and counts of successes and failures are at least 5 in both samples. Therefore, we can compute the z-test statistic.

c. What is the p-value for this test?

d. What would you conclude from this test at 5% level of significance?