TERM STAT*2040 TEST II PRACTICE PACKAGE
Winter 2012
DISCLAIMER
This resource is not designed to be used independently of the SLG Session listed above. Please use this resource for referral only it is supplemental review and is not meant to be a substitute for lecture or textbook material, or individual studying. This document may contain errors, which may not be apparent unless, or even if, you attend the session for which it is intended. This document has not been approved or endorsed by, nor is it affiliated with, the Department of Mathematics & Statistics.
Instructions:
Print out and complete the following questions. For best results, do the mock midterm under exam conditions (quiet & without notes). The solutions will be taken up in the following sessions:
LEADER Katherine Kim & Zo
TIME Thursday, March 15 10-11:30 AM
th
PLACE LIB 120A: (behind Research Help) LIB 384
Monday, March 19th 7-10 PM
As A Reminder...
These questions are intended to be additional practice, and to work with the other resources available. Lab TA's Prof Balka The Math and Stats Help Room (Library, Third Floor) Your Assignments, Quizzes, Lecture Notes, Course Notes
xkcd.com
1. Which of the following statements is false? A) The standard error of the mean is the standard deviation of the sampling distribution of sample means and is represented by the symbol xbar . B) You can only use z as an approximation of your test statistic when is known, and the population you are sampling from is normally distributed. C) The larger the sample size, the smaller the margin of error. D) If x is normally distributed then xbar is normally distributed. E) None of the above
2. If Guelph housing prices are known to have a mean of $389000 and a standard deviation of $120000, find the probability that a randomly picked house costs more than $400000 (assuming normal distribution). A) 0.0917 B) 0.408 C) 0.4641 D) 0.0359 E) None of the above
3. A drug company recently created a new drug that they believed would help lower blood cholesterol. This would be an important drug as it is unhealthy to have high levels of cholesterol in the blood. It is universally agreed that a blood cholesterol level of 5.7 is unhealthy. In order to test their drug, the company administered their drug to a patient with high cholesterol. The following is a series of measurements of that patient's cholesterol after the drug was administered. 5.7, 4.5, 5.8, 4.9, 5.4, 5.2, 6.1, 5.0 Based on this information, do a hypothesis test to show whether or not this drug does in fact lower blood cholesterol at a 0.05 level of significance. Assume that = 0.50 and that blood cholesterol levels are normally distributed among the population. A) We reject the null hypothesis at a 0.05 level of significance because p> B) We accept the null hypothesis at a 0.05 level of significance because p> C) We reject the null hypothesis at a 0.05 level of significance because p< D) We accept the null hypothesis at a 0.05 level of significance because p< E) None of the above
4. Which of the following statements about p-values is false? A) We say that the evidence against Ho is significant at the level of significance if the p-value B)The smaller the p-value, the stronger the evidence against Ho C) A p-value is the probability of getting the observed test statistic, or a value with even more evidence against the null hypothesis, if the null hypothesis is true D) If the alternative is Ha: > o, the p-value is the area to the right of the test statistic value. E) None of the above (they are all true)
5. The average time it takes for an adult male between the ages of 20-22 to run one kilometer is 4.2min. Andrew, student at the University of Guelph saw this statistic in the local newspaper, and decided to make it his goal to run a kilometer 3 times a week in order to become faster than average. The following are the results of a series of time trials after one month of training: 4.0, 3.8, 3.6, 4.3, 3.9, 3.7 Do these time trials provide strong evidence that running 3 times a week for one month can make you a faster than average runner? (Assume a 0.05 level of significance.) A) There is strong evidence that this training has made Andrew's running time shorter than 4.2min/km because p< B) There is not strong evidence that this training has made Andrew's running time shorter than 4.2min/km because p< C) There is strong evidence that this training has made Andrew's running time shorter than 4.2min/km because p> D) There is not strong evidence that this training has made Andrew's running time shorter than 4.2min/km because p> E) None of the above
6. Which one of the following statements about (correctly constructed) 95% confidence intervals for the mean is FALSE? (A) For a given sample, the 90% confidence interval will be narrower than the 95% confidence interval. (B) For a given sample, the probability the sample mean will be captured by the 95% confidence interval is 0.95. (C) A confidence interval will tend to get narrower as the sample size increases. (D) In repeated sampling, we would expect 5% of the 95% confidence intervals calculated to fail to capture the population mean. (E) If a t value is required to calculate a 95% confidence interval, the t value will be larger if the sample size is n = 10 than if it is n = 20.
WARNING: The next three questions are based on the following information. A random sample of the weight of 16 fish from the Grand River gave the following statistics: sample mean = 58.9, sample standard deviation = 12.4. 7. The estimated standard error of the sample mean is: (A) 0.775 (B) 3.1 (C) 3.6 (D) 9.61 (E) 12.4 8. If the weights of the fish are considered normally distributed, a 95% confidence interval for the population mean based on this sample is: (A) (53.8, 64.0) (B) (53.5, (C) 64.3) (52.8, 65.0) (D) (52.3, 65.5) (E) (49.8, 68.0)
9.
Dr. Vissen at the University of Guelph believes that the fish from the Grand River are mutating due to exposure to toxic mutagens, and thus growing into monster fish-men bent on world domination. Looking at an old field report from 1997, he finds that the generally accepted mean weight of a fish from the Grand was 51.3. Looking at the sample data obtained above, what can we conclude at the 0.05 confidence level? (choose the closest value) (A) Build a bunker and stock up on food! (the fish are growing, p = 0.007) (B) The world is safe. For now. (the fish are not growing, p = 0.007) (C) We're screwed. (the fish are growing, p = 0.013 ) (D) Dr. Vissen has read one too many comic books. (the fish are not growing, p = 0.013) (E) The weight is actually decreasing.
10. Kim is doing her stats assignment late one night. She does a hypothesis test and chooses to reject the null hypothesis at the 0.05 level. How many of the following statements are false? i. ii. iii. iv. v. She would definitely reject the null hypothesis at the 0.10 level. The p-value could be 0.02 The p-value could be 0.08 She will definitely reject the null hypothesis at the 0.01 level. A p-value is the probability that our null is true. (A) 4 (B) 3 (C) 2 (D) 1 (E) 0
11. The grades of 16 students who go to SLGs are compared to 16 randomly selected students who do not. The students who attend SLGs have a mean grade of 74.4 with a sample standard deviation of 1.6. While those who do not have a mean grade of 70.6.with a sample standard deviation of 1.7. Construct a 95% confidence interval for the difference between the two means. (A) (3.8, -3.8) (B) (1.2, 6.6) (C) (2.9, 4.7) (D) (2.2, 4.7) (E) (2.9, 4.2)
12. A student wants to test the null hypothesis H0 : = 123 against the Ha : 123. She doesn't include the p-value in her paper but includes confidence intervals. She gives a 95% confidence interval of (118.12, 121.80), and a 99% confidence interval of (116.32, 123.53). Which one of the following could be the p-value of the appropriate test? (A) 0.0029 (B) 0.0458 (C) 0.0580 (D) 0.0002 (E) 1.8143 13. If the alternative hypothesis is Ha : 270 what values of z will lead to a rejection of the null hypothesis at the 5% significance level? (A) z > 1.645 (B) z < 1.645 (C) | z| > 1.645 (D) | z| < 1.96 (E) | z| > 1.96
14. The following output from R is produced:
Pooled-Variance Two-Sample t-Test data: x: zinc with group = A , and y: zinc with group = B t = -1.1059, df = 37, p-value = 0.2759 alternative hypothesis: difference in means is not equal to 0 95 percent confidence interval: -0.21964765 0.06454239 sample estimates: mean of x mean of y 1.3235 1.401053
Based on this data what would be the best statement made about these findings.
See next page
(A) The null hypothesis is false based on a p-vale of 0.2759. There is a difference between the mean values of zinc in groups A and B. (B) The alternative hypothesis is true based on a p-value of 0.2759. There is a significant difference between the means of the two groups, with group B having a higher content than A. (C) There is little evidence to suggest that the null hypothesis is false, based on a p-value of 0.2759. Therefore, there is little evidence to suggest that there is a difference between mean the zinc concentrations for group A and B. (D) The alternative hypothesis is false. The groups have no difference in the mean zinc concentrations.
15. If sigma () for the population is known, you would use a: (A) Standard Normal Distribution with no degrees of freedom (B) Standard Normal Distribution with degrees of freedom specific to the question (C) T-distribution with no degrees of freedom (D) T-distribution with degrees of freedom specific to the question (E) I'm a genius.... I'll create my own distribution.
16. The Central Limit Theorem states that as the number of sample size increases, the distribution of the sample mean becomes less and less skewed. (A) True (B) False
17. A call centre is experimenting with improving their customer service by occasionally having a human operator pick up a call directly. The centre claims that 15% of phone calls are answered by a human operator. Assuming the company's claim is true, what is the probability that in 20 calls at randomly selected times, no more than 1 is answered directly by a human operator? (A) 0.12 (B) 0.14 (C) 0.16 (D) 0.18 (E) 0.20
18. Which one of the following statements is true? (A) The t distribution is exactly equal to the standard normal distribution for sample sizes that are less than 30. (B) The standard normal distribution has less area in the tails than the t distribution. (C) When calculating a confidence interval for a single mean, all else being equal, as the degrees of freedom increase, the margin of error increases. (D) The t distribution gets closer to the standard normal distribution as the degrees of freedom decrease. (E) E) None of the above 19. Diane wants to change her confidence interval from 95% to 99%. What is the only thing that should change in her confidence interval calculation? (A) Nothing.... it is all the same (B) The x bar of the calculation, (C) Margin of error (D) The standard deviation (E) The point estimate
20. Let the continuous random variable X have the uniform distribution with a lower bound of 15 and an upper bound of 105. What is the conditional probability X is less than 20, given X is less than 45. (A) 0.10 (B) 0.125 (C) 0.25 (D) 0.20 (E) 0.40
21. If we wish to test the null hypothesis that the population means of RDI for day shift and night shift workers are equal, what is the value of the appropriate test statistic? Assume that the populations are normall distributed, and that the two populations have the same variance. (A) 3.5 (B) 3.7 (C) 3.9 (D) 4.1 (E) 4.3