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Questions on First Level Statistics- Some have been omitted that you are not responsible for 1-6 omit 7. A 95% confidence interval for the population average is interpreted to mean that , prior to obtaining the data, there is a .95 probability that the interval will contain the A. population mean B. population C. sample mean D. sample standard deviation E. population standard deviation 8. 9. If the level of confidence is kept constant, what happens to the width of the confidence interval as the sample size decreases? A. It depends on the parameter being estimated. B. It remains the same. C. It decreases. D. It increases. E. It could increase or decrease depending on the value of the point estimate. 10. According to the Central Limit theorem, the sampling distribution of sample means will approach a normal distribution if _________________. A. the population follows the binomial distribution B. the sample size is small (usually < 30) C. the standard error is large (usually 30 or more) D. the sample size is large (usually 30 or more) or population follows the normal distribution E. the sample is taken independently of the population. 11. A. B. C. D. E. In a statistical test of hypothesis, a type I error is ____________________ rejecting the null hypothesis when in fact the null hypothesis is true accepting the null hypothesis when in fact the alternative hypothesis is true rejecting the null hypothesis when in fact the alternative hypothesis is true taking too small a sample to reach a conclusion accepting the null hypothesis when in fact the null hypothesis is true 12. In a statistical test of hypothesis, a type II error is ____________________ A. accepting the null hypothesis when in fact the null hypothesis is true B. rejecting the null hypothesis when in fact the null hypothesis is true C. taking too small a sample to reach a conclusion D. rejecting the null hypothesis when in fact the alternative hypothesis is true E. accepting the null hypothesis when in fact the alternative hypothesis is true 13. The average monthly expenditure on liability insurance per physician is determined by selecting a random sample of 16 physicians. The sample mean is $645 and the sample standard deviation is $215. What is the 95% confidence interval for the mean monthly expenditure per physician on liability insurance, assuming monthly expenditures are normally distributed? A. B. C. D. E. 576.2 to 713.8 506.8 to 783.4 561.0 to 762.0 530.5 to 759.5 539.7 to 750.4 14. What element of a statistical test of hypothesis would be affected by changing the significance level (alpha)? A. Test statistic B. Rejection region C. Standard error D. Null hypothesis E. Alternative hypothesis 15. When using the p-value to arrive at a conclusion for a test of hypothesis, the null hypothesis will be rejected if the p- value is _________. A. less than alpha B. greater than the level of significance C. not equal to alpha D. greater than alpha E. equal to alpha 16. Four hundred students will take second-level business statistics this year (undergraduate and graduate). A sample of 50 students were asked to rate this exam on a scale of 1 to 10 (1=outstanding, 10=terrible). The sample showed a mean rating of 8.4 with a standard deviation of 2.55. The cruel statistics professor will use this exam only if the average rating is above 8.0 in the population. What is the alternative hypothesis for testing that the exam will be used? A. Ha: u <= 8 D. Ha: u = 8 B. Ha: u < 8 E. Ha: u >= 8 C. Ha: u > 8 17. (Refer to #16) What is the value of the test statistic? A. .16 B. .06 C. 1.96 D. 1.11 E. 1.65 18. 19. For fixed probability of a type I error, as the sample size increases, A. the standard deviation of the population decreases. B. the probability of a type II error decreases. C. the probability of a type II error increases. D. the size of the critical (rejection) region decreases. E. the power of the test is not affected. 20. 1. E 2. C 3. D 4. B 5. D 6. E Find the value of X such that Pr(X > ? ) = .60 7. A 8. 9. D 10. D 11. A 12. E 13. D Find C.I. for mu. Xbar =645, s=215, n=16, use t(15, 0.025) 14. B 15. A 16. C 17. D t = (ybar-mu)/(s / square root of n) = (8.4 – 8) / (2.55 / 7.07) 18. 19. B 20. B Ha mu > 70. Find Pr(ybar > 69.8) = Pr (t > -2) with 24 d.f. Questions 21-40 are concerned with the following situation. An experimenter wishes to compare the sales of two restaurants. She randomly selects eleven days from last year and records the sales of each restaurant on those days. The data (in thousands of dollars) are: Day Restaurant 1 2 3 4 5 6 7 8 9 10 11 1:2.15, 2.16, 2.13, 2.25, 2.20, 2.18, 2.27, 2.21, 2.23, 2.16, 2.20 2:2.32, 2.34, 2.30, 2.40, 2.34, 2.20, 2.42, 2.36, 2.36, 2.30, 2.34 The following statistics were calculated: restaurant 1 restaurant 2 difference sample mean 2.195 2.335 -0.140 sample std. 0.04 0.06 0.04 sample size 11 11 11 sample pooled standard deviation, sp= 0.05 21. 22. 23. 24. 25. 26. 27. A 95% confidence interval for the population average is interpreted to mean that , prior to obtaining the data, there is a .95 probability of the ____________________ A. population mean being in that interval B. population being within the interval. C. sample mean being in that interval D. sample standard deviation being in that interval E. population standard deviation being in that interval 28. 29. If the level of significance is held constant, what happens to the probability of a type II error as the sample size decreases? A. It depends on the parameter being estimated. B. It remains the same. C. It decreases. D. It increases. E. It could increase or decrease depending on the value of the point estimate. 30. 31. In a statistical test of hypothesis, claiming that the mean daily sales of restaurant one equals $2000 when in fact the mean daily sales differs from $2,000 is a(n) ____________________ A. indication that you need to get out more often (Hint: this is a wrong answer). B. a type II error C. a type I error. D. a correct decision. E. the level of significance. 32. The level of significance, alpha, when testing that "the mean sales are the same for the two restaurants" would be A. the probability of finding a difference when no difference exists. B. the probability of not finding a difference when no difference exists. C. the probability of finding a difference when a difference exists. D. the probability of not finding a difference when a difference exists. E. the same as the p-value. 33. What is the 95% confidence interval for the mean daily sales for restaurant 2, assuming monthly sales are normally distributed? A. 0.04 to 0.06 B. 2.30 to 2.37 C. 3.14 to 3.18 D. 2000 to 3000 E. impossible to calculate given the sample information. 34. Given the null hypothesis is true, the probability of finding a value that is more contradictory of the null hypothesis than the test statistic value is called the ______________ ? A. critical value B. Rejection region C. alpha D. p-value E. Alternative hypothesis 35. What you wish to prove goes in the ____________ hypothesis. A. critical value. B. Rejection region. C. Null hypothesis. D. p-value. E. Alternative hypothesis. 36. 37. Using the sample data above, suppose you wish to test the alternative hypothesis that the mean sales of restaurant 2 exceeds $2,100, what would be the rejection region if alpha = 0.05? A. Reject the null hypothesis if the test statistic > t(10, 0.025) or < -t(10, 0.025) B. Reject the null hypothesis if the test statistic > Z(0.025) or < -Z(0.025) C. Reject the null hypothesis if the test statistic > t(10, 0.05) D. Reject the null hypothesis if the test statistic > Z(11, 0.05) E. Reject the null hypothesis if the test statistic > t(20, 0.025) or < -t(20, 0.025) 38. Can the two independent sample t-test of means be used to test equality of the mean daily sales for the two restaurants? A. No, because the sample sizes are too small. B. Yes, because the data is from two independent random sample of days. C. No, because the sample variances are not equal. D. Yes, because there are two means. E. No, because the data comes from the same eleven days. 39. 40. The degrees of freedom of the t-distribution are the same as the degrees of freedom of A. the standard normal distribution. B. the estimate of the population variance. C. the population mean. D. alpha E. the binomial. Answers 21. 22. 23. 24. 25. 26. 27. a 28. a 29, d as you know less about the population the chance of error increases 30. c 31. b 32. a 33 b use t with 10 d.f., ybar = 2.335, s = 0.06 and n=11 34 d definition page 56 of text book 35. e 36. b 37. C 38. E samples come from the same 11 days and therefore not independent 39. 40. b degrees of freedom of the t always comes from the estimate of the variance