front 1 Find the critical value z _{α} _{/2} that corresponds to the given confidence level. 99% | back 1 z _{α} _{/2 }= 2.575 |
front 2 Express the confidence interval 0.222 < 0.444 in the form p̂ ± E. | back 2 p̂ ± E = 0.333 ± 0.111 p̂ = (upper + lower confidence limit) ÷ 2 = (0.444 + 0.222) ÷ 2 = 0.333 E = (upper – lower confidence limit) ÷ 2 = (0.444 – 0.222) ÷ 2 = 0.111 |
front 3 A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 320 babies were born, and 256 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective? | back 3 0.742 < p < 0.858 Yes, the proportion of girls is significantly different from 0.5. |
front 4 A genetic experiment with peas resulted in one sample of offspring that consisted of 415 green peas and 159 yellow peas.
| back 4 0.240 < p < 0.314 No, the confidence interval includes 0.25, so the true percentage could easily equal 25% |
front 5 In a poll of 546 human resource professionals, 39.4% said that body piercings and tattoos were big grooming red flags.
| back 5 a. 215 546 x 39.4% = 215.124 b. 0.340 < p < 0.448 c. 0.367 < p < 0.421 d. The 99% confidence interval is wider than the 80% confidence interval. As the confidence interval widens, the probability that the confidence interval actually does contain the population parameter increases. |
front 6 During a period of 11 years 1074 of the people selected for grand jury duty were sampled, and 42% of them were immigrants. Use the sample data to construct a 99% confidence interval estimate of the proportion of grand jury members who were immigrants. Given that among the people eligible for jury duty, 54.7% of them were immigrants, does it appear that the jury selection process was somehow biased against immigrants? | back 6 0.381 < p < 0.459 Yes, the confidence interval does not include the true percentage of immigrants. |
front 7 Use the given data to find the minimum sample size required to estimate a population proportion or percentage. Margin of error: 0.03; confidence level 90%; p̂ and q^ unknown | back 7 n = 752 |
front 8 Use the given data to find the minimum sample size required to estimate a population proportion or percentage. Margin of error: four percentage points; confidence level 95%; from a prior study, p̂ is estimated by the decimal equivalent of 54% | back 8 n = 597 |
front 9 A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.04 with 99% confidence if a) she uses a previous estimate of 0.52? b) she does not use any prior estimates? | back 9 a) n = 1035 b) n = 1037 |
front 10 The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the brand. How many adults must he survey in order to be 80% confident that his estimate is within six percentage points of the true population percentage?
| back 10 a) n = 114 b) n = 49 c) No, a sample of students at the nearest college is a convenience sample, not a simple random sample, so it is very possible that the results would not be representative of the population of adults. Just surveying the adults at the nearest college is a convenience sample, which is not necessarily representative of the population. |
front 11 Which concept below is NOT a main idea of estimating a population proportion?
| back 11 Using a sample statistic to estimate the population proportion is utilizing descriptive statistics. Using a sample statistic to estimate the population proportion is not utilizing descriptive statistics; it is utilizing inferential statistics. |
front 12 Which of the following is NOT an observation about critical values?
| back 12 A critical value is the area in the right-tail region of the standard normal curve. A critical value is a z-score associated with the area in the right-tail region of the standard normal curve, not the area itself. |
front 13 When analyzing polls, which of the following is NOT a consideration?
| back 13 The sample should be a voluntary response or convenience sample. The sample should be a simple random sample as voluntary response or convenience samples introduce bias and reduce the reliability of any poll results. |