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Unformatted text preview: nfidence Intervals True / False Questions 1-611 Chapter 01 - An Introduction to Business Statistics 1. The t distribution always has n degrees of freedom. True False 2. When the margin of error is added to and subtracted from the sample mean an interval is formed that will contain µ with probability of (1 - α). True False 3. The standard error of the sample mean is s/√n. True False 4. Assuming the same level of significance α, as the sample size increases, the value of tα/2approaches the value of zα/2. True False 5. When constructing a confidence interval for a sample proportion, the t distribution is appropriate if the sample size is small. True False 6. First a 90% confidence interval is constructed from a sample size of 100. Then, for the same identical data, a 92% confidence interval is constructed. The width of the 90% interval is wider than the 92% confidence interval. True False 1-612 Chapter 01 - An Introduction to Business Statistics 7. When the population is normally distributed and the population standard deviation σ is unknown, then for any sample size n, the sampling distribution of is based on the z distribution. True False 8. When the sample size and sample standard deviation remain the same, a 99% confidence interval for a population mean, µ will be narrower than the 95% confidence interval for µ. True False 9. When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n = 100 will be narrower than a confidence interval for a population mean based on a sample of n = 50. True False 10. When the level of confidence and the sample size remain the same, a confidence interval for a population mean µ will be wider, when the sample standard deviation s is small than when s is large. True False 11. When the level of confidence and sample proportion remain the same, a confidence interval for a population proportion p based on a sample of n = 100 will be wider than a confidence interval for p based on a sample of n = 400. True False 12. When the level of confidence and sample size remain the same, a confidence interval for a population proportion p will be narrower when is larger than when is smaller. True False 1-613 Chapter 01 - An Introduction to Business Statistics 13. When solving for the sample size needed to compute a 95% confidence interval for a population proportion "p", having a given error bound "B", we choose a value of makes as small as reasonably possible. True False that 14. When determining the sample size n, if the value found for n is 79.2, we would choose to sample 79 observations. True False Multiple Choice Questions 15. The t distribution approaches the _______________ as the sample size ___________. A. Binomial, increases B. Binomial, decreases C. Z, decreases D. Z, increases 16. The width of a confidence interval will be: A. Narrower for 99% confidence than 95% confidence. B. Wider for a sample size of 100 than for a sample size of 50. C. Narrower for 90% confidence than 95% confidence. D. Wider when the sample standard deviation (s) is small than when s is large. 17. As standard deviation increases, samples size _____________ to achieve a specified level of confidence. A. Increases B. Decreases C. Remains the same 1-614 Chapter 01 - An Introduction to Business Statistics 18. When determining the sample size, if the value found is not an integer initially, the next highest integer value will ____________ be chosen. A. Always B. Sometimes C. Never 19. When constructing a confidence interval for a population mean, if a population is normally distributed and a small sample is taken, then the distribution of _____ distribution. A. z B. t C. Neither D. Both A and B 20. A confidence interval increases in width as A. The level of confidence increases B. n decreases C. s increases D. All of the above 21. The width of a confidence interval will be: A. Narrower for 98% confidence than for 90% confidence. B. Wider for a sample size of 64 than for a sample size of 36. C. Wider for a 99% confidence than for 95% confidence. D. Narrower for sample size of 25 than for a sample size of 36. E. None of the above. 1-615 is based on Chapter 01 - An Introduction to Business Statistics 22. A Research and Development Laboratory researcher for a paint company is measuring the level a certain chemical contained in a certain type of paint. If the paint contains too much of this chemical, the quality of the paint will be compromised. On the average, each can of paint contains 10% of the chemical, How many cans of paint should the sample contain if the researcher wants to be 98% certain of being within 1% of the true proportion of this chemical? A. 4887 B. 1107 C. 26 D. 645 23. Which of the following is an advantage of confidence interval estimate over a point estimate for a population parameter? A. Interval estimates are more precise than point estimates. B. Interval estimates are less accurate than point estimates. C. Interval estimat...
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