4.01 Quiz: Confidence Intervals and Hypothesis Tests for a Single Population Proportion

Which of the following is not a condition that must be met before you can use a z-procedure to conduct a hypothesis test about a single population proportion?

p0p-hat ≥ 10

Management at a sparkling water factory has designed a new system it thinks will lower the proportion, currently at .12, of incorrectly labeled bottles. In the year following the implementation of the new system, quality control engineers randomly sample 378 bottles and find 40 that are labeled incorrectly. What are the test statistic and the P-value for the significance test H0: p = .12 Ha: p < .12? (Find the P-value for this test using your normal probability table.)

z = -.8484 p = .1977

The staff at an aquarium with 500,000 annual visitors wants to know whether there's a difference in the proportion of its patrons who come specifically for workshops and those who come for other reasons. The staff takes a random exit poll of 1,238 visitors, and 751 say they came for workshops. For a significance test of H0: p = 0.5 Ha: p ≠ 0.5, what are your test statistic and your P-value? Use your TI-83 calculator to get your P-value.

z = 7.5, p≈ 0

Management at a sparkling water factory has designed a new system it thinks will lower the proportion, currently at .12, of incorrectly labeled bottles. In the year following the implementation of the new system, quality control engineers randomly sample 378 bottles and find 40 that are labeled incorrectly. Which of these hypotheses tests whether the proportion of incorrectly labeled bottles has decreased?

H0: p = .12 Ha: p < .12

The staff at an aquarium with 500,000 annual visitors wants to know whether there's a difference in the proportion of its patrons who come specifically for workshops and those who come for other reasons. The staff takes a random exit poll of 1,238 visitors, and 751 say they came for workshops. What are the hypotheses for your test?

H0: p = 0.5 Ha: p ≠ 0.5

Which of the following is a proper set of hypotheses for a test about a single population proportion?

H0: p = p0 Ha: p < p0

Suppose you record 83 successes out of a random sample of 200 drawn from a population that yielded a proportion of successes of .40 in a previous study. If you were to calculate a standardized test statistic for a hypothesis test about the population proportion, where H subscript 0 : p subscript 0 equals.40, what would your standard deviation of p with hat on top look like?

√.40(.60)/200

Suppose you record 83 successes out of a random sample of 200 drawn from a population that yielded a proportion of successes of .40 in a previous study. If you were to construct a confidence interval for the population proportion of your sample, what would your standard error of p with hat on toplook like?

√.415(.585)/200

The staff at an aquarium with 500,000 annual visitors wants to know whether there's a difference in the proportion of its patrons who come specifically for workshops and those who come for other reasons. The staff takes a random exit poll of 1,238 visitors, and 751 say they came for workshops. For the test statistic used in a test of the hypotheses H0: p = 0.5 Ha: p ≠ 0.5, what's the standard deviation of p with hat on top ?

.0142

Management at a sparkling water factory has designed a new system it thinks will lower the proportion, currently at .12, of incorrectly labeled bottles. In the year following the implementation of the new system, quality control engineers randomly sample 378 bottles and find 40 that are labeled incorrectly. What standard deviation would you use for a test statistic in the hypothesis test H0: p = .12 Ha: p < .12

.0167