Question

1. For a particular scenario, we wish to test the hypothesis H₀ : p = 0.48. For a sample of size 50, the sample proportion p̂ is 0.42. Compute the value of the test statistic z_obs. (Express your answer as a decimal rounded to two decimal places.)

2. Which of the following is a valid alternative hypothesis for a one-sided hypothesis test about a population proportion p?

A. p = 0.6

B. p < 0

C. p ≠ 0.7

D. p > 0.3

3. Suppose that the sample proportion p̂ is used to construct a confidence interval for the population proportion p. Assuming that the value of p̂ is fixed, which of the following combinations of confidence levels and sample sizes yield the the widest confidence interval (that is, one with the largest range of values)?

A. 95% confidence level, n = 500

B. 95% confidence level, n = 50

C. 99% confidence level, n = 50

D. 99% confidence level, n = 500

4. Which of the following statements about a confidence interval is NOT true?

A. A confidence interval of size α indicates that there is a probability of α that the parameter of interest falls inside the interval.

B. A confidence interval is generally constructed by taking a point estimate plus or minus the margin of error.

C. A confidence interval is often more informative than a point estimate because it accounts for sampling variability.

D. A confidence interval provides a range of plausible values for a parameter based on the sampling distribution of a point estimator.

5. For a test of H₀ : p = p_{0 vs.} H₁ : p < p₀, the value of the test statistic z _obs is -0.87. What is the p-value of the hypothesis test? (Express your answer as a decimal rounded to three decimal places.)

6. A pilot survey reveals that a certain population proportion p is likely close to 0.37. For a more thorough follow-up survey, it is desired for the margin of error to be no more than 0.03 (with 95% confidence). Assuming that the data from the pilot survey are reliable, what sample size is necessary to achieve this? (Express your answer as an integer, rounded as appropriate.)​​​​​​​

7. Suppose that you are testing whether a coin is fair. The hypotheses for this test are H₀: p = 0.5 and H₁: p ≠ 0.5. Which of the following would be a type II error?

A. Concluding that the coin is not fair when in reality the coin is not fair.

B. Concluding that the coin is fair when in reality the coin is fair.

C. Concluding that the coin is not fair when in reality the coin is fair.

D. Concluding that the coin is fair when in reality the coin is not fair.

Answer 1