MCQ Confidence intervals PDF

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EC1011: Data Analysis II – Multiple Choice Questions Topic 2: Confidence Interval Estimation

1. Which of the following factors do not affect the width of the confidence interval? A. B. C. D.

Sample mean Population variance Sample size Confidence level

2. Given a sample of size 30 taken in order to estimate the population mean, use the t-table to find the value of A for the probability P(|t|  A) = 0.01. E. F. G. H.

2.247 2.756 2.462 2.750

3. The 𝑧-value needed to construct 92.5% confidence interval estimate for the difference between two population proportions is A. B. C. D.

2.58 2.33 1.96 1.78

4. Suppose that I want to calculate the 80% confidence interval for the mean value of a normally distributed population with a known variance σ = 40. Which of the following critical values should I use to perform this calculation? A. B. C. D.

± 1.645 ± 1.28 80% critical value of the t with 39 degrees of freedom 80% critical value of t with 40 degrees of freedom

5. A company finds that forty out of a random sample of 200 e-mail messages sent by employees were not business related. Which of the following statements is correct? A. B. C. D.

The upper limit of the 95% confidence interval could be less than 0.15 The lower limit of the 95% confidence interval could be less than 0.15 The upper limit of the 90% confidence interval could be less than 0.15 The upper limit of the 98% confidence interval could be less than 0.15

6. The population proportion (𝑃) is 0.70 and the sample size is ‘large’. What is the probability that the sample proportion (𝑝 ) is less than 0.6? A. B. C. D.

0.5019 0.297 0.5300 0.7019

7. A 95% confidence interval estimate for the difference between two population means, 1   2 , is determined to be (62.75, 68.52.) If the confidence level is reduced to 90%, the confidence interval A. B. C. D.

becomes wider remains the same becomes narrower more information is needed

8. Which of the following statements is false? A. To cut the width of a confidence interval in half, one has to double the sample size B. In determining the necessary sample size in making an interval estimate for a population mean, it is first necessary to first make an estimate of the population standard deviation C. In the formula n  z2 / 2   2 / ME 2 , ME represents half the width of the confidence interval D. None of the above

9. Which of the following is not a part of the formula for constructing a confidence interval for the difference between two population means? A. B. C. D.

A point estimate of the difference between the population means The standard error of the sampling distribution of the sample means The confidence level The values of the population means

10. The z - value needed to construct 97.8% confidence interval estimate for the difference between two population proportions is A. B. C. D.

11.

2.29 2.02 1.96 1.65

In constructing a 95% confidence interval estimate for the difference between the means of two normally distributed populations, where the unknown population variances are assumed not to be equal, summary statistics computed from two independent samples are as follows: n1  50 , x1  175, s1  18.5 , n2  42 , x2  158 , and s2  32.4 . The upper confidence limit is: A. B. C. D.

19.123 28.212 24.911 5.788

12. The values associated with a two-sided 95% confidence interval of the standard normal distribution are A. B. C. D.

± 1.28 ± 1.645 ± 1.96 ± 2.575

13. The values associated with a two-sided 90% of the Student’s t distribution and 73 degrees of freedom are A. B. C. D.

± 1.319 ± 1.96 ± 2.96 ± 1.67

14. If the population proportion is 0.90 and a sample of size 64 is taken, what is the probability that the sample proportion is less than 0.88? A. B. C. D.

0.5019 0.2981 0.6300 0.7019

15. Suppose that a population has a mean of 870 and a variance of 1,600. If a random sample of 25 is drawn from the population, the probability that the sample mean is greater than 875 is A. B. C. D.

0.9544 0.8413 0.2676 0.5899 Pr (

𝑋 − 870 875 − 870 ) = 𝑃𝑟(𝑍 > 0.625) = 1 − 𝑃𝑟(𝑍 < 0.625) = > 40 40 √25 √25 1 − 𝑃𝑟(𝑍 < 0.625) = 1 − 0.7324 = 0.2676

Answers: 1. A 2. B 3. D 4. B 5. B 6. B 7. C 8. A 9. D 10. A 11. B 12. C 13. D 14. B 15. C...