This quiz works best with JavaScript enabled. Home > Ugc Net > Paper 1 > Research Stats > Confidence Intervals – Quiz 2 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Confidence Intervals Quiz 2 (30 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. We want to know if students work too much (and thus spend less time on their classes). Previous studies show that the standard deviation for work time is 3 hours, and a survey of 40 students has a mean of 9.8 work hours. The 95% confidence interval is ..... A) (8.84, 10.76). B) (9.00, 10.60). C) (8.87, 10.73). D) (9.02, 10.58). Show Answer Correct Answer: C) (8.87, 10.73). 2. Find the value of E, the margin of error, for c = 0.90, n = 16 and s = 2.4. A) 1.05. B) 2.54. C) 0.08. D) 0.26. Show Answer Correct Answer: A) 1.05. 3. Which of the following sources of error is included in the margin of error A) Chance variation in choosing a random sample. B) Undercoverage. C) Some of the subjects did not understand the questions. D) Voluntary response. Show Answer Correct Answer: A) Chance variation in choosing a random sample. 4. Use the t table to find the critical value.98% confident, df = 10 A) 2.82. B) 2.40. C) 2.76. D) 2.36. Show Answer Correct Answer: C) 2.76. 5. Why do we use a t-distribution instead of a z-distribution for means? A) It reflects greater variability present in small samples. B) It allows us to decrease the margin of error without increasing our confidence level. C) It allows us to use the population standard deviation. D) None of these. Show Answer Correct Answer: A) It reflects greater variability present in small samples. 6. A quality control specialist at a glass factory must estimate the mean clarity rating for a new batch of glass using a sample of 18 glass sheets from the batch. Past investigations show that clarity ratings are normally distributed. The specialist decides to use a t-distribution rather than a z-distribution because ..... A) The t distribution is more accurate than a z distribution. B) Clarity ratings for the entire bacth are normally distributed. C) The t-distribution will create a narrower interval than z. D) The standard deviation for the population is unknown. Show Answer Correct Answer: D) The standard deviation for the population is unknown. 7. A researcher wishes to determine the mean energy consumption of a new light bulb. She takes a random sample of 41 bulbs and determines that the mean consumption is 1.3 watts per hour with a standard deviation of 0.7. When constructing a 97% confidence interval, which would be the most appropriate value of the critical value? A) 2.807. B) 2.25. C) 2.072. D) 2.704. Show Answer Correct Answer: B) 2.25. 8. What critical value t* is used in constructing a 99% confidence interval based on n = 12 randomly selected observations. A) 1.96. B) 3.106. C) 2.58. D) 3.055. Show Answer Correct Answer: B) 3.106. 9. A recent study of 750 Internet users in Europe found that 35% of Internet users were women. What is the 95% confidence interval of the true proportion of women in Europe who use the Internet? A) 0.316 < p < 0.384. B) 0.321 < p < 0.379. C) 0.309 < p < 0.391. D) 0.305 < p < 0.395. Show Answer Correct Answer: A) 0.316 < p < 0.384. 10. A person selects a random sample of 15 credit cards and determines the annual interest rate, in percent, of each one. The sample mean is 12.42 with a sample standard deviation of 1.3. It is desired to construct a 90% Confidence Interval.Find the Standard Error to three decimal places. A) 0.336. B) 13.156. C) 0.33566. D) 0.087. Show Answer Correct Answer: A) 0.336. 11. Use the margin of error, confidence level, and standard deviation $ \sigma$ to find the minimum sample, n, required to estimate an unknown population mean $ \mu$ .Margin of Error = $ 134Confidence level = 95% $ \sigma$ =$ 542 A) 44. B) 63. C) 109. D) 62. Show Answer Correct Answer: B) 63. 12. Which of the following changes to a study would result in a narrower confidence interval? A) Increasing the confidence level, increasing the sample size. B) Decreasing the confidence level, increasing the sample size. C) Decreasing the confidence level, decreasing the sample size. D) Increasing the confidence level, decreasing the sample size. Show Answer Correct Answer: B) Decreasing the confidence level, increasing the sample size. 13. Use the t table to find the critical value.95% confident, sample size = 8 A) 1.86. B) 1.89. C) 2.31. D) 2.36. Show Answer Correct Answer: D) 2.36. 14. A random sample of 100 WHS students found that 53 of them were in possession of a pencil. What is the p-hat ( population proportion percentage) for this sample? A) 1. B) 0.5. C) 0.47. D) 0.53. Show Answer Correct Answer: D) 0.53. 15. Which of the following is NOT a common confidence level? A) 100%. B) 90%. C) 99%. D) 95%. Show Answer Correct Answer: A) 100%. 16. A random sample of 9 refrigerators has a mean cost of $ 1263 and a standard deviation of $ 530.75. Construct a 90% confidence interval for the average cost of a refrigerator. A) (605.19, 1921.47). B) (933.93, 1592.40). C) (650, 2300). D) (934.26, 1921.47). Show Answer Correct Answer: B) (933.93, 1592.40). 17. The 90% interval for a statistics test was given by 72 +-7. What is the lower bound for the interval? A) 72. B) 7. C) 79. D) 65. Show Answer Correct Answer: D) 65. 18. What is the degrees of freedom equal to? A) 1-n. B) N-1. C) N. D) N+1. Show Answer Correct Answer: B) N-1. 19. Increasing the sample size ..... the confidence interval. A) Increases. B) Decreases. C) There is not enough evidence to determine the answer. D) Does not affect. Show Answer Correct Answer: B) Decreases. 20. A research group wishes to estimate the mean amount of time (in hours) that members of a fitness center spend exercising each week. They want to estimate the mean within a margin of error of 0.5 hours with a 95% level of confidence. Previous data suggests that the standard deviation of the population is 2.2. Which of the following is the smallest sample size they could use? A) 60. B) 90. C) 180. D) 75. Show Answer Correct Answer: D) 75. 21. A random sample of 20 cupcakes found the interval for average calories to be (150, 350). Which is the correct interpretation of the 95% confidence interval? A) We are 95% confident that the true mean caloric content can be found with a sample of 150 to 350 cupcakes. B) We are 95% confident that the interval 150 to 350 calories captures the true average caloric content. C) We are 95% confident that a sample of 20 cupcakes will find 250 calories per cupcake. D) None of these are correct. Show Answer Correct Answer: B) We are 95% confident that the interval 150 to 350 calories captures the true average caloric content. 22. In a survey of 250 Internet users, 195 have high-speed Internet access at home. Find a 90% confidence interval for the proportion of all Internet users who have high-speed Internet access at home. A) (0.737, 0.823). B) (0.731, 0.829). C) (0.728, 0.832). D) (1.19, 1.38). Show Answer Correct Answer: A) (0.737, 0.823). 23. You take a poll and find that 34% of the 100 people you asked dislike school lunches. Using a 95% confidence level, what is the margin of error? A) 0.047. B) .34. C) .034. D) 0.093. Show Answer Correct Answer: D) 0.093. 24. A random sample of 42 textbooks has a mean price of $ 114.50 and a standard deviation of $ 12.30. Find a 98% confidence interval for the mean price of all textbooks. A) (111.38, 117.62). B) (109.61, 119.39). C) (110.08, 118.92). D) (110.78, 118.22). Show Answer Correct Answer: C) (110.08, 118.92). 25. An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.What is the point estimate? A) 0.90. B) 75. C) 105.2. D) 10. Show Answer Correct Answer: C) 105.2. 26. An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.What is the point estimate?(that is the number before the $ \pm$ symbol) A) 0.90. B) 105.2. C) 10. D) 75. Show Answer Correct Answer: B) 105.2. 27. Find the critical value, tc for c = 0.99 and n = 10. A) 3.250. B) 2.262. C) 3.169. D) 1.254. Show Answer Correct Answer: A) 3.250. 28. Which of the following changes to a study would result in a smaller confidence interval? A) Increasing the confidence level, increasing the sample size. B) Increasing the confidence level, decreasing the sample size. C) Decreasing the confidence level, decreasing the sample size. D) Decreasing the confidence level, increasing the sample size. Show Answer Correct Answer: D) Decreasing the confidence level, increasing the sample size. 29. Find the Critical Value( z*) for an 86% Confidence Level. Be careful. A) 1.282. B) -1.47. C) -1.48. D) 1.48. Show Answer Correct Answer: D) 1.48. 30. Suppose an interval is (.62, .70). Margin of error = A) .08. B) .04. C) .74. D) .66. 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