Stat 303 Practice Exam #2 with Problems and Solutions, Exams of Data Analysis & Statistical Methods

Download Stat 303 Practice Exam #2 with Problems and Solutions and more Exams Data Analysis & Statistical Methods in PDF only on Docsity! STAT 303 Sections 511 Fall 2008 Practice EXAM #2 Instructor: Jiawei Wei Oct. 08, 2008 1 Z Table Z Table: Negative Values Body of table gives area under Z curve to the left of z. Example: P[Z < -2.63] = .0043 z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 -3.80 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 -3.70 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 -3.60 .0002 .0002 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 -3.50 .0002 .0002 .0002 .0002 .0002 .0002 .0002 .0002 .0002 .0002 -3.40 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0002 -3.30 .0005 .0005 .0005 .0004 .0004 .0004 .0004 .0004 .0004 .0003 -3.20 .0007 .0007 .0006 .0006 .0006 .0006 .0006 .0005 .0005 .0005 -3.10 .0010 .0009 .0009 .0009 .0008 .0008 .0008 .0008 .0007 .0007 -3.00 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010 -2.90 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014 -2.80 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019 -2.70 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .0026 -2.60 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 .0037 .0036 -2.50 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048 -2.40 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064 -2.30 .0107 .0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .0084 -2.20 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110 -2.10 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143 -2.00 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183 -1.90 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .0233 -1.80 .0359 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294 -1.70 .0446 .0436 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .0367 -1.60 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455 -1.50 .0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .0559 -1.40 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0694 .0681 -1.30 .0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0838 .0823 -1.20 .1151 .1131 .1112 .1093 .1075 .1056 .1038 .1020 .1003 .0985 -1.10 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170 -1.00 .1587 .1562 .1539 .1515 .1492 .1469 .1446 .1423 .1401 .1379 -0.90 .1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611 -0.80 .2119 .2090 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .1867 -0.70 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .2148 -0.60 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451 -0.50 .3085 .3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .2776 -0.40 .3446 .3409 .3372 .3336 .3300 .3264 .3228 .3192 .3156 .3121 -0.30 .3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .3483 -0.20 .4207 .4168 .4129 .4090 .4052 .4013 .3974 .3936 .3897 .3859 -0.10 .4602 .4562 .4522 .4483 .4443 .4404 .4364 .4325 .4286 .4247 0.00 .5000 .4960 .4920 .4880 .4840 .4801 .4761 .4721 .4681 .4641 2 5. Using the distribution above, how likely are you to get two 4’s OR a two 5’s if you sample randomly? A. 0.0125 B. 0.15 C. 0.000025 D. 0.005 E. 0.0225 6. Suppose you’re testing 0H : μ = 5 vs. aH : μ > 5 and you get a p-value = 0.036. Which of the following is/are correct? A. 5 is NOT less than 3.6, so we fail to reject. B. The true mean is significantly greater than 5 at the 5% level. C. We can’t say the true mean is significantly greater than 5 at the 5% level. D. We can’t say the true mean is significantly greater than 5 at the 10% level. E. Two of the above are correct. 7. Suppose a sample proportion based on samples of size 50, p  N(0.75, 0.06122). What is the smallest proportion in the TOP 5%? A. 0.753 B. 0.649 C. 0.872 D. 0.870 E. 0.851 8. Let X  N(7.2, 1.42). If we take a random sample of size 49 from this population, what is the distribution of the sample mean, X ? A. Since the sample size is large, > 30, we can say the distribution will be approximately normal with the same mean and standard deviation. B. Since the original data is normal, we can say the distribution will be exactly normal with the same mean and standard deviation. C. Since the sample size is large, > 30, we can say the distribution will be approximately normal with the mean = 7.2 and standard deviation = 1.4/ 49 . D. Since the original data is normal, we can say the distribution will be exactly normal with the mean = 7.2 and standard deviation = 1.4/ 49 . E. X  N(7.2, 0.0292). 5 9. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200. The mean score for U.S. college students is about 115 with a standard deviation of about 30. A teacher who suspects that older students have better attitudes toward school gives the SSHA to 25 students who are at least 30 years of age. This sample produces a mean score of 132.2. What set of hypotheses should the teacher use to prove she is correct about older students’ attitudes? A. 0H : μ = 132.2 vs. aH : μ 132.2 B. 0H : μ = 132 vs. aH : μ > 132.2 C. 0H : μ = 115 vs. aH : μ 115 D. 0H : μ = 115 vs. aH : μ > 115 E. 0H : μ = 132 vs. aH : μ > 115 10. Using the same scenario in the last question, which of the following would be considered a Type I error? A. The teacher concludes that older students are smarter than the general population of U.S. students. B. The teacher concludes that older students have better attitudes than the general population of U.S. students. C. The teacher fails to prove that older students have better attitudes than the general population of U.S. students when actually their attitudes are better. D. The teacher concludes that older students have better attitudes than the general population of U.S. students when actually their attitudes are better. E. The teacher concludes that older students have better attitudes than the general population of U.S. students when actually their attitudes are not any better. 11. A 95% confidence interval of 14 to 17 means that A. 95% of the time the true mean will be between 14 and 17. B. 95% of the confidence intervals calculated like this one will contain the true mean. C. 95% of the true means will be between 14 and 17. D. All of the above are correct. E. None of the above is correct. 12. Why do we call the distribution of the sample mean, X , a sampling distribution? A. because it’s the distribution of the sample of random observations B. because we must take a sample just to get one random observation C. because we sample from the distribution to find the sample mean D. because the distribution is only of a sample, not the whole population E. because we can’t get the distribution of the whole population of sample means, only samples 6 13. If we think of the null hypothesis as there is no fire and a fire alarm going off as claiming there IS a fire, what would a false alarm correspond to? A. a correct decision since the fire department must respond to every alarm B. a Type I error because we rejected 0H C. a Type II error because we rejected 0H D. a Type I error because we failed to reject 0H E. a Type II error because we failed to reject 0H 14. Margin of error can be reduced by? A. Increasing . B. Increasing *z . C. Increasing n. D. Increasing confidence level. E. None of above. 15. Suppose we test the following: 0H : μ = 20 vs. aH : μ > 20, where μ is the mean tree height in feet in Yosemite national park. 20 trees were randomly selected and measured. The p-value for the test statistic was 0.23. Your boss wants to know what the number 0.23 means. A. It is the probability that the null hypothesis is true. B. It is the probability of making a Type I error. C. It is the probability of making a Type II error. D. It is how many standard deviations your statistic was from the claimed parameter value of 20. E. None of the above is correct. 16. A certain population follows a normal distribution with mean μ and standard deviation  = 2.5. You collect data and test the hypotheses: 0H : μ = 1 aH : μ1 You obtain a p-value of 0.022. Which of the following is true? A. A 95% CI for μ will include the value 1. B. A 95% CI for μ will include the value 0. C. A 99% CI for μ will include the value 1. D. A 99% CI for μ will include the value 0. E. We can’t determine since we can’t relate confidence intervals to tests of hypotheses. 17. Why is the Central Limit Theorem so important in the study of statistics? A. It allows us to use the normal distribution for any kind of data. B. It tells us that any data can be approximately normal if we take a large enough sample. C. It tells us that any sample mean can be approximately normal. D. It tells us that any sample mean will be unbiased. E. None of the above is true statement of the CLT. 7