VIEWS: 20 PAGES: 5 POSTED ON: 8/2/2011
Practice Problems 1) A population has a mean of 45 and a standard deviation of 5. Find the z-scores of the following raw scores: a) score = 47 b) score = 48 c) score = 40 d) score = 39 2) A population has a mean of 45 and a standard deviation of 5. Find the raw scores of the following z- scores: a) z-score = 1.3 b) z-score = -0.4 c) z-score = 0 d) z-score = -1.5 3) The following table shows the scores of subject 1 on six different scales of an aptitude test. Also shown are the means and standard deviations of these scales. Test Mean Standard Deviation Score Z-Score Clerical Ability 50 15 41 Logical Reasoning 40 4 47 Mechanical Ability 120 25 100 Numerical Reasoning 100 10 105 Spatial Relations 70 20 90 Verbal Fluency 60 6 70 a) Calculate the z-scores for each. b) On which test did subject 1 score the highest? Which did subject 1 score the lowest? Practice Problems 4.) Convert the following test scores to z-scores and then decide which is the student’s best and worst area of performance. a) Best:___________________________________ Worst:_____________________________ Test Score Mean Standard Deviation Z-Score Oral Interpretation 38 40 10 Persuasion 28 20 20 Theory Building 45 30 20 b.) Best:___________________________________ Worst:________________________ Test Score Mean Standard Deviation Z-Score BUS 205 60 80 8 ECN 201 92 78 15 ECN 202 85 75 10 5.) Convert the following test scores to z-scores and then decide which is the student’s best and worst area of performance. a) Best:________________________________ Worst:_____________________________ Test Score Mean Standard Deviation Z-Score English 87 80 5 Science 90 92 16 History 75 55 18 b) Best:___________________________________ Worst:_____________________________ Test Score Mean Standard Deviation Z-Score BUS 205 38 50 18 ECN 201 28 15 21 ACC 101 45 20 16 c) Best:___________________________________ Worst:_____________________________ Test Score Mean Standard Deviation Z-Score CIS 100 48 35 20 WRT 100 38 22 30 BUS 100 55 19 15 6.) Under regular circumstances the population of 2-year old children has an average weight of 26 lbs. The distribution of weights is normal with a standard deviation of 2. The researcher, who thinks that children will weigh more with extra handling, selects a random sample of n = 4 newborn infants, instructs the parents to provide each child with extra handling, and then records the weight of each child at age 2. The average weight of the sample is 29.5 lbs. a) What are the IV?_____________________________________ DV?_________________________ b) What is the hypothesis (words)?_______________________________________________________ c) What is the testable hypothesis (numerically)?___________________________________________ d) What is the critical region? ____________________________________________________ e) What is the z-test for this infant?____________________________________________________ f) Graph the distribution, critical area, and shade in where the z-test needs to lie in order for the hypothesis to be proven true. g) Do you accept or reject the hypothesis? Z-Test Extra Practice Problems 7.) In each of the sections of BUS 205, the instructor handed out different study guides to see if different study guides would make a difference in students’ grades on the exam. All four sections of BUS 205’s test #1 were scored and the average for the first exam was a 75 across all sections with a standard deviation of 5. The instructor wanted to know if her section first section of BUS 205 was different from the population of BUS 205 students in her sections. The scores for the exam were as follows for section 1: 75, 90, 85, 60, 55. a) What are the IV?_____________________________________ DV?_________________________ b) What is the hypothesis (words)?_______________________________________________________ c) What is the testable hypothesis (numerically)?___________________________________________ d) What is the null hypothesis (words)?_____________________________________________________ e) What is the null hypothesis (numerically)?________________________________________________ f) What is the critical region? ____________________________________________________ g) What is the z-test?____________________________________________________ h) Graph the distribution, critical area, and shade in where the z-test needs to lie in order for the hypothesis to be proven true. g) Do you accept or reject the hypothesis? 8.) The HR department of DWE wanted to know if their orientation was helping managers better understand the rules of the company. The HR department knew that if an employee read the manual s/he would have a better understanding of company rules. Half of the managers participated in the orientation where they were given the manual to read and the other half of the mangers did not participate nor were they given a manual. The managers were then given a survey to see if they were able to answer different rules of the company. The following table is a listing of their scores. Managers in Managers not in Orientation Orientation 75 80 63 65 88 90 69 45 72 82 a) What are the IV?_____________________________________ DV?_________________________ b) What is the hypothesis (words)?_______________________________________________________ c) What is the testable hypothesis (numerically)?___________________________________________ d) What is the null hypothesis (words)?_____________________________________________________ e) What is the null hypothesis (numerically)?________________________________________________ f) What is the critical region? ____________________________________________________ g) What is the z-test?____________________________________________________ h) Graph the distribution, critical area, and shade in where the z-test needs to lie in order for the hypothesis to be proven true. g) Do you accept or reject the hypothesis?