D2L Quizzes * = Correct Answer Quiz Adjustment Values The following values will be added to the quiz score for each Quiz. Quiz 1 2 3 4 5 6 7 8 9 +---+---+---+---+---+---+---+---+---+ Value | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | | +---+---+---+---+---+---+---+---+---+ The two lowest quiz scores will be dropped. Quiz 1 Sept 8 - 13 1. A clinical trial where neither the subject nor the subjects doctor knows whether the subject is in the treatment or control group is called a ___________ trial. a. controlled *b. double blind c. observational d. scientific 2. What is the SPSS measure for a continuous variable? a. compact b. granular c. interval *d. scale 3. What is the SPSS measure for a categorical variable? a. discrete *b. nominal c. ordinal d. singular 4. Using the Tukey's Hinges method of computation, what is Q3 for this dataset? 2 3 5 7 11 13 17 a. 7 b. 11 *c. 12 d. 15 5. Which of these datasets has at least one mild or extreme outlier? a. 118 123 b. 118 123 188 c. 18 118 123 188 *d. None of the above Quiz 2 Sept 15 - 20 1. Which of the following is not affected by outliers if the dataset size is greater than or equal to 5? *a. interquartile range b. mean c. range d. standard deviation 2. The percentage of observations in a histogram bin is proportional to the ___________ of the histogram rectangle over that bin. Not all of the histogram widths are necessarily the same. *a. area b. height c. perimeter d. width 3. A histogram has two bins. The first bin is defined by [20, 30) and contains 80% of the observations. The second bin is defined by [30, 70) and contains 20% of the observations. Estimate the median of the histogram by using linear interpolation. a. 25.00 *b. 26.25 c. 27.75 d. 50.00 4. Find the mean of the histogram in Problem 3. a. 25 *b. 30 c. 35 d. 40 5. Recall that to compute SD you divide by n to when computing the standard deviation of a dataset; when computing SD+, you divide by n - 1. If SD = 5.0 and n = 20, what is SD+? a. 4.88 *b. 5.13 c. 5.60 d.6.00 Quiz 3 Sept 22 - 27 1. For a standard normal population (mu=0, sigma=1), what percent of the observations are between -0.33 and 1.16? Remember: to convert the proportion given by the standard normal table to a percent, multiply the proportion by 100. a. 25% *b. 51% c. 62% d. 88% 2. For a standard normal population (mu=0, sigma=1), what percent of the observations are greater than 2.27? a. 0.6% b. 1.2% c. 2.4% d. 4.8% 3. For a standard normal population, find z such that the percent of area between -z and z is 88%. a. 0.655 b. 1.055 *c. 1.555 d. 2.575 4. Find the 99th percentile of IQ scores. For IQ scores, the mean = 100 and SD = 15. *a. 135 b. 140 c. 142 d. 145 5. Corrected Problem: A random sample of the weights of baby mice at birth have sample mean = 1.0 gram and sample SD = 0.2 gram. The size of the random sample is 64. Find a 95% confidence interval for the birth weight of the "ideal mouse" that nature is trying to produce. Use [-1.96, 1.96] as the confidence interval for a standard normal z. Correct answer: [0.951, 1.049] Quiz 4 Sept 29 to Oct 4 1. 25 measurements are made of the speed of light. The average of the measurements is 299,792 km/sec with SD+ = 10 km/sec. Find a 95% confidence interval for the true speed of light, based on these measurements. a. [299,970.0, 200,974.0] *b. [299,788.08, 299,795.92] c. [299,782.0, 299,802.0] d. [299,772.4, 299,811.6] 2. If IQ scores are normally distributed with mean = 100 and standard deviation = 15, about how many persons out of 1 billion have an IQ score greater than 190? *a. 1 b. 5 c. 12 d. 29 3. If the sample size n = 4, what are the expected normal scores computed using Van der Waerden's method. *a. -0.84 -0.25 0.25 0.84 b. -0.84 -0.25 0.00 0.25 0.84 c. -0.96 -0.43 0.43 0.96 d. -0.96 -0.43 0.00 0.43 0.96 4. What is the range of the possible sample correlations for a dataset? a. [0, 1] b. [-0.5, 0.5] *c. [-1, 1] d. (-infinity, +infinity) 5. The correlation indicates the amount of _____________ between two variables. a. association b. causality c. disassociation *d. linear association When the quiz was first posted, Answer d was shown as "linear correlation". Choosing d in that case would be been a circular defininition, so credit is also given for a. Quiz 5 Oct 13 to Oct 18 1. An event is a __________ of the sample space. a. closure b. element c. product d. subset 2. A random variable that has two outcomes 0 and 1, with probabilities 1 - p and p, respectively, is a ___________ random variable. a. Bernoulli b. Cauchy c. normal d. Poisson 3. The chance of winning a lottery game is 0.0002. What is the chance of winning the lottery at least once if you buy 5000 tickets? Assume that the chance of winning with any particular lottery ticket is independent of the chance of winning with any other lottery ticket. Hint: see Example 19 in the Oct 12 Lecture notes. a. 0% b. 9% c. 37% *d. 63% 4. A discrete random variable x has outcomes 1, 5, and 10 with probabilities 0.4, 0.5, and 0.1, respectively. What is the expected value of x? a. 2.0 b. 2.4 *c. 3.9 d. 5.0 5. The odds that the New England Patriots win the Super Bowl in 2017 is 7 to 2 (if the Patriots win the Super Bowl, you win $7; if the Patriots lose, you lose $2). If this is a fair bet, what is the probability that the Patriots win the Super Bowl in 2017? Hint: See Review Problem 3 in the Oct 12 Lecture Notes. a. 15% *b. 22% c. 29% d. 33% Quiz 6 Oct 20 to 25 1. What is the theoretical standard deviation of a Bernoulli random variable with probability of success 0.64? a. 0.14 *b. 0.48 c. 0.64 d. 0.80 2. A random variable x has expected value 10 and theoretical standard deviation 5. What is the expected value of the sum of 64 independent outcomes of x? a. 64 b. 128 *c. 640 d. 1,280 3. A random variable x has expected value 10 and theoretical standard deviation 5. What is the theoretical standard deviation of the sum of 64 independent outcomes of x? a. 5 *b. 40 c. 80 d. 320 4. The law of averages works by ___________ . Hint: see the Law of Averages section in the Oct 12 Notes. a. accumulation b. compensation c. counterbalancing *d. swamping 5. When performing a test of hypothesis to see whether a single die is fair for rolling a 1, the null hypothesis (H0) assumes that a. the estimated proportion phat is exactly 1/6. b. the population density p is exactly 0. c. the population proportion p is exactly 1. *d. the true probability of rolling a 1 is 1/6. Quiz 7 Oct 27 to Nov 1 1. A 5%-level one-sample z-test (95% confidence) uses which two-sided confidence interval for the test statistic to decide whether to accept or reject the null hypothesis? a. [-1.65, 1.65] *b. [-1.96, 1.96] c. [-2.35, 2.35] d. [-2.96, 2.96] 2. When performing a one-sample t-test, if the sample size is 14, then __________ degrees of freedom should be used for determining the confidence interval from the t-table. a. 1 *b. 13 c. 14 d. 15 3. Suppose that you perform a paired two-sample t-test on two groups with variable names x and y. This is the same as performing a(n) ______________ on the sample with variable name diff = x - y. a. independent two-sample t-test *b. one-sample t-test c. one-sample z-test d. one-sample z-test for a sum 4. True/false question: Perform a one-sample t-test with the following information: H0: mu = 100 n = 9 xbar = 105 SD+ = 6 You should reject the null hypothesis H0. *a. True b. False 5. For this problem, see the Review Exercise 8 in the Oct 16 Notes. A geometric probability distribution has probability of success p = 0.80. What is the expected value? a. 1 b. 2 *c. 4 d. 6 Quiz 8 Nov 10 to Nov 15 1. Using the standard normal table, find a 98% confidence interval. *a. [-1.64, 1.64] b. [-1.96, 1.96] c. [-2.05, 2.05] d. [-2.33, 2.33] 2. A 1%-level statistical test uses a ______________ confidence interval for the test statistic. a. 50% b. 95% *c. 99% d. 99.5% 3. A random sample contains the values 111 105 85 102 Find the test statistic t for testing whether the null hypothesis that the random sample comes from a population that has mean = 100. Use a 95% confidence interval for the test statistic. Hint: Use SPSS to perform the t-test. *a. 0.135 b. 0.173 c. 0.239 d. 0.865 4. A paired-sample t-test is preferred over an independent-sample t-test if the a. degrees of freedom is larger for the paired-sample t-test. b. measures of the variables for both groups is nominal (categorical). c. number of subjects in Group 1 is not equal to the number of subjects in Group 2. *d. pairing of the subjects between the two groups reduces the variability. 5. Find a 95% confidence interval for a chi-squared test statistic with 3 degrees of freedom. a. [0, 5.99] b. [-5.99, 5.99] *c. [0, 7.81] d. [-7.81, 7.81] Quiz 9 will be posted tonight. 1. For which of these sample spaces is letter independent of number? a. {A1, A2, A3, A4, B1, B2} b. {A1, A2, A3, B4, B5, B6} c. {A1, A3, A4, B1, B2, B4} *d. {A1, A2, B1, B2, C1, C2} 2. A place kicker in the national football league makes kicks of length 50 yards with 60% probability. What is the probability of making 4 or more kicks out of 5 attempts? a. 8% b. 20% *c. 34% d. 60% 3. A dataset is a sample with values drawn from an ideal measurement model Use the t-table to find a 99% confidence interval for the true value of the mean. Here are the sample statistics: n = 10 xbar = 3.4 SD+ = 0.8. a. [0.80, 6.00] b. [1.34, 5.46] c. [1.83, 4.97] *d. [2.6, 4.2] 4. The probability of rejecting the null hypothesis if the null hypothesis is true is the ____________ of the test. a. degrees of freedom *b. level c. magnitude d. response 5. The technique of estimating a confidence interval by resampling the original sample with replacement is *a. bootstrapping b. clustering c. transformation d.translation Review Quiz 1. What are the degrees of freedom for a one sample t-test with sample size n = 18? a. 16 *b. 17 c. 18 d. 19 2. What are the degrees of freedom for a paired 2-sample t-test with 13 observations in Group A and 13 observations in Group B? *a. 12 b. 13 c. 15 d. 16 3. What are the degrees of freedom for an independent 2-sample t-test with 17 observations in Group A and 13 observations in Group B? a. 12 b. 13 *c. 28 d. 29 4. The table of observed values for a chi-squared goodness-of-fit test has 10 cells. What are the degrees of freedom for this test? a. 1 b. 8 *c. 9 d. 10 5. The table of observed values for a chi-squared test of independence has 5 rows and 3 columns. What are the degrees of freedom for this test? a. 1 *b. 8 c. 13 d. 15 6. What type of t-test should be used to test whether a new drug reduces cholesterol? *a. Independent 2-sample t-test b. Paired 2-sample t-test 7. Which type of t-test should be used to test whether heights and weights of identical twins significantly different? a. Independent 2-sample t-test *b. Paired 2-sample t-test 8. Which type of t-test should be used to test which of two new web sites under development is more user friendly? a. Independent 2-sample t-test. *b. Paired 2-sample t-test.