The practice questions are divided into two, related, sets of multiple-­‐choice questions. The first sect concerns the SAMPLING DISTRIBUTION FOR THE POPULATION PROPORTION (9 questions). The second set concerns the CONFIDENCE INTERVAL FOR THE POPULATION PROPORTION (22 questions). Answers are provided on pages 2 and 6. SAMPLING DISTRIBUTION THE POPULATION PROPORTION (REVIEW) 1. True or False? The approximate normality of the sampling distribution becomes valid much more quickly (with increasing sample size) when the population proportion is moderate rather than extreme. 2. What is the minimum sample size that produces a sampling distribution for p-­‐
hat that is approximately normal when the population proportion is p=0.05? a. 5 b. 10 c. 11 d. 100 e. 200 Answer questions 3-­‐5 below assuming that you have a sample of 50 from a population with p = 0.8 3. True or False? The sampling distribution will be approximately normal in this case. 4. The mean value of the sampling distribution for the population proportion is a. 0.50 b. 0.80 c. 0.90 d. 0.95 e. 0.99 5. The variance of the sampling distribution for the population proportion is: a. 0.0032 b. 0.0050 c. 0.057 d. 0.071 Suppose that 25% of students support the Green Party at St Mary’s University (SMU). Answer questions 6-­‐9 below assuming that you have a random sample of 100 students from SMU. 6. What is the mean of the sampling distribution? a. 0.25 b. 0.50 c. 0.95 d. 0.99 7. What is the standard deviation of the sampling distribution? a. 0.0025 b. 0.0500 c. 0.0187 d. 0.0433 8. What is the probability that the sample proportion will be > 30%? a. 0.8749 b. 0.1357 c. 0.1251 d. 0.0433 9. What is the 95th percentile of the sample proportions? a. 1.645 b. 0.321 c. -­‐0.321 d. -­‐1.645 Question: 1 2 3 4 5 6 7 8 9 Answer: True e True b a a d c b CONFIDENCE INTERVALS FOR THE POPULATION PROPORTION 1. True or False? For any confidence level, C, the value of the sample proportion will always be considered a plausible value for p. 2. True or False? The Normal approximation to the sampling distribution for a population proportion will be adequate for a study with a sample size of 25 and a proportion of 0.9. 3. In a real world problem, the probability that a sample-­‐based estimate of the proportion (𝑝) is exactly equal to the true parameter (p) is: a. Available within a z table b. 0 c. 1 d. impossible to know 4. For a sample size of 81 and a sample proportion of 0.1, the 90% confidence interval on a number line is: a. (-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐|-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐) 0.100 0.1 0.900 b. (-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐|-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐) 0.350 0.1 0.165 c. (-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐|-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐) 1.545 0.1 1.745 d. (-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐|-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐) 0.450 0.1 0.155 5. What is the relationship between the confidence level and the width of the confidence interval? a. They are identical b. They have a positive relationship c. They have a negative relationship d. They are independent The Pew Research Centre for the People and the Press reported a poll result finding 322 out of 1149 randomly selected voters would not vote for a political candidate who disagreed on their views about gay marriage. Answer questions 6-­‐9 below based on this poll. 6. True or False? The conditions have been met for constructing a confidence interval for p. 7. What is the estimated standard deviation of the sample proportion? a. 0.0147 b. 0.0002 c. 0.0132 d. 0.0001 8. The margin of error for this poll at the 95% confidence level is: a. ± 2.6% b. ± 1.32% c. ± 0.0132 d. ± 1.96 9. The 95% CI for the proportion of voters who will not vote for a candidate who disagrees with their view on gay marriage. a. 0.28 ± 2.6% b. 0.28 ± 0.026 c. 0.28 ± 0.0132 d. 0.28 ± 1.96 Drug use among twelfth grad high school students is increasing. A recent study focused on the use of ecstasy (MDMA) and found 32% reported using this drug at least once in a random sample of 200 local twelfth grade students. Answer questions 10-­‐13 below based on this study. 10. True or False? Is it appropriate to use a Z-­‐interval to estimate a range of plausible values for the population proportion? 11. What is the standard error of the sample proportion? a. 1.96 b. 2.576 c. 0.085 d. 0.033 12. The margin of error for this poll at the 99% confidence level is: a. ± 0.085 b. ± 0.065 c. ± 1.96% d. ± 2.576% 13. The 99% CI for the proportion twelfth grade students who have use MDMA at least once is: a. (0.595, 0.765) b. (0.294, 0.346) c. (0.235, 0.405) d. (0.255, 0.385) 14. If the confidence level (C) increases, the value of alpha (α). a. decreases b. increases c. stays the same 15. Two ways to decrease the margin of error are: ∗
a. decrease 𝑧!/!
or decrease samples size (n) ∗
b. increase 𝑧!/! or increase samples size (n) ∗
c. decrease 𝑧!/!
or increase samples size (n) ∗
d. increase 𝑧!/! or decrease samples size (n) The following statements (17-­‐21 below) are attempts to interpret the 95% CI (16.8% ±1.1%) for the proportion of HPV infection among Canadian females. For questions 17-­‐21 indicate if each statement is correct by responding with True or False. 16. 16.8% of all Canadian females are infected with HPV. 17. The most likely proportion of Canadian females infected with HPV is 16.8% 18. We don’t know the true proportion of Canadian females infected with HPV, but we know that it’s within the interval (15.7%, 17.9%). 19. There is a 95% chance that the true proportion of Canadian females infected with HPV is with the interval (15.7%, 17.9%). 20. With repeated sampling, a confidence interval of this level will contain the true value 95 out of 100 times. 21. Your supervisor wants you to increase the confidence level from 95% to 99% without decreasing precision. How would you do this? a.
increase ME ∗
b.
increase 𝑧!/!
c.
increase n d.
decree ME ∗
e.
decrease 𝑧!/!
f.
decrease n 22. A new poll is being widely reported in the news as having a margin of error of plus or minus 3 percentage points. We are not told the confidence level, but we are told that the sample proportion was 37% and the size for the poll was 1000. What is the confidence level for this poll? a. 50 b. 90 c. 95 d. 99 e. 196.5 Question: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Answer: True False b d b True c a b True d a c a c False False False False True c c