VIEWS: 4 PAGES: 11 POSTED ON: 9/24/2011
Practice Exam I - Calculator 440/640 Experimental Methods Spring, 2009 For calculation problems, start with the appropriate formula and show all the gory details. 1) Explain the role of inferential statistics in terms of samples and populations? 2) Which of the following is not the same sort of thing: {variance, median, range, standard deviation} and why? 3) Why do psychologists need to know statistics? 4) A study is conducted where a person’s average mood is measured as a function of body height. There are three happiness categories: happy, angry and sad. What is the independent variable? What is the dependent variable? What kind of scale is the independent variable on? What kind of scale is the dependent variable on? 5) Which is not a valid equation? n n n a. (X i Yi ) X i Yi i1 i1 i1 n b. C i n *C i1 n n n c. (X i Yi ) X Yi2 2 2 i i1 i1 i1 n n d. C * X i C * X i i1 i1 1 N N 6) Show that (X i C) X i NC i1 i1 7) Draw the histogram for this frequency distribution. What is the mode? interval frequency 10 to 19 5 20 to 29 8 30 to 39 13 40 to 49 3 50 to 59 7 60 to 69 2 70 to 80 1 8) What is the sum of all the column heights in a relative frequency distribution? a. Infinity b. It depends on the probabilities c. 1 d. 2.71828182845… 9) What is the difference between a simple frequency distribution and a grouped frequency distribution? 2 10) A group of third grade wrestlers have weights: 60, 60, 62, 62, 62, 65, 65, 66, 67, 68, 69,70,70,71, and 83 pounds. Which wrestler(s) is (are) at the 75th percentile? 11) In problem 8, what is the median? 12) What is the relationship between the variance and the standard deviation? 13) In a positively skewed distribution, which is likely to be larger? a. The mode b. The median c. The mean d. One is not likely to be larger than the other 14) Calculate the biased standard deviation , for the data in problem 10. Start with the appropriate formula and show your calculation. 15) What is the purpose of calculating a z score? 16) Given the data in question 10, what are the a. Mean Z _____________ b. Standard deviation of Zs _____________ c. Variance of Zs _____________ 17) If resting heart rate is normally distributed in the population with μ = 72 and σ = 8, what is the percentile rank (approximately) of someone whose resting 3 heart rate is 82? 18) What does the central limit theorem tell us? 19) All normal distributions can be described using the following equation: 1 2 2 f (X) e(X ) / 2 2 2 On the right hand side of the equation, which symbols are constants, which are variables and which are parameters? Hint: the parameters are those, which determine the location and width of the normal distribution. 20) What is the null hypothesis? 21) Which represents an area under part of the standard normal distribution curve? a. z b. c. p d. and p 22) Heart rates for a group of 25 joggers were measured, and the mean of the group was found to be 65 bpm. If the mean of the population is 72 bpm with a standard deviation of 10, what is the z-score for this group compared to other groups of the same size? Do Joggers have a significantly lower heart rate than the general population? Assume an of .05. 4 23) How does one get the sample distribution of the means from the distribution of the single scores? _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ 24) What is an alpha level? _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ 25) Explain the effects of alpha and N on type I and type II errors. _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ 26) A researcher tests a random sample of 25 college students to see how many hours they spend each day at the computer. The sample mean is 1.25 hours. If the population mean for this variable is .75 hours with a standard deviation of .4, what is the z-score for this group of college students (as compared to other groups the same size)? 27) What is the relationship between the z distribution and the t distribution? How many t distributions are there? How many z distributions are there? _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ 28) When do we need to use the t-test instead of the z-test? _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ 29) When N is large we are more likely to accept our alternative hypothesis in a t test. There are two reasons for this. What are they? Hint: what is the effect of N on t and tcrit? _______________________________________________________________ 5 _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ 30) Suppose you are computing a 95% confidence interval. What are you 95% confident of? _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ 31) Ace drug company is developing a new drug for depression. It is called Happyol. Pilot tests show that 20mg of Happyol works best on average. The standard deviation of optimal doses was 5mg in the same pilot tests. However, Ace needs to know how good of an estimate 20mg is with respect to the optimal dose for the entire population. Ace plans to conduct extended trials to prove that 20mg is 95% likely to be the true mean optimal dose, plus or minus 1.0 mg. How many patients do they need in their extended study? 32) A group of students who agreed not to watch television for six months is asked how many books (other than those required for school) each read during that time period. The data are as follows: 7, 3, 8, 1, 2, 8, 4, 3, 0, 5. If the population mean for the number of nonrequired books read in six months by students the same age is 2.0, are the non-tv watchers exceptional? 33) The marketing department of a manufacturing company wanted to find out how many blank video cassettes are purchased by the average American each year. The data for a random sample of Americans are as follows: 7, 0, 6, 3, 10, 0, 4, 9, 6, 3, 12, 0, 5, 1, 8, 6. What are the limits of the 99% confidence interval for the mean of the population? 6 34) In practice, the t test for two independent means is often more practical than the one sample t-test and the one sample z-test. Why is this? _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ 35) When should the pooled variance t-test be used? When should the separate variance test be used? _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ 36) Given the following data: X 1 = 8; X 2 = 5; s1 = 2; s2 = 3;N1 = 10; N2 = 15, what does the separate-variances t equal? Is the difference between means significant? 37) Given the following data: 1 = 9; 2 = 6; s1 = 2; s2 = 1.5;N1 = 16; N2 = 21, what does the pooled-variances t equal? Is the difference between means significant? 7 38) What is statistical power? How might having statistical power lead to misinterpreted results? _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ 39) Define type I and type II errors. _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ 40) What does it mean to say “an effect is significant?” 41) In statistical power analysis, what do 1 , , and d represent? How are they affected by n, 1 2 , and ? 42) In an experiment that tests a single sample of 40 subjects against a hypothesized population mean, what would be your statistical power when dealing with an effect size d of .3 and performing an =.05 two tailed test? 43) What is the purpose of linear correlation? 44) When developing the formula for correlation, why do we map raw scores into z values? 8 45) Suppose that 2 variables X and Y are closely related by the equation Y=X2. Is linear correlation a good tool for discovering such a relationship? Why? What about Y=aX+b? 46) For the data below, what is the value of correlation coefficient r? X Y 5 4 6 3 8 6 9 6 4 4 47) Given a correlation coefficient of -.52 from two variables measured on 14 subjects, are the variables significantly correlated? 48) What is the purpose of linear regression? 49) In linear regression, the predicted value of Y, given X, is based on a weighted average of 2 distinct tendencies. What are they? 9 50) To show that the number of hours spent studying can, to some degree, predict scores on a quiz, a professor collected the data presented below: Study Quiz Score Hours 7 5 6 10 11 6 5 4 15 9 11 10 12 8 11 9 7 7 Determine the regression equation and predict the score of a student that studies 0 hours. 51) Under which circumstances do you apply each test or analysis? a. One sample z-test b. One sample t-test c. Confidence interval of a mean d. z-test for two independent sample means e. t-test for two independent samples (separate variances) f. t-test for two independent samples (pooled variances) g. Linear correlation h. t-test of Pearson’s r i. Linear regression 52) Extra credit: Prove that XY 1 XY NXY N 1 x y r N x y sx sy 10 11