1. During class we mentioned that sometimes the scale of a variable (measurement) might be subjective depending on how it is measured. (Note that in this case subjective does not mean arbitrary). Please provide an example where measuring a variable, a concept or an attribute could be measured using these scales: nominal, ordinal and interval or ratio. You may reach concepts outside education or social sciences. (2 points)
2. A superintendent and her statistician are discussing about how to explore some new data that they collected among their students. Please address the following:
2.1 The superintendent and her statistician are discussing how to explore a set of nominal variables. The superintendent propose to run a histogram and a pie chart. What should the statistician recommend her?(1 point)
2.2. The superintendent and her statistician are discussing how to explore a set of nominal variables. The statistician suggest to calculate the mode and the median. Is he correct? Explain why? (1 point)
2.3 The superintendent and her statistician are discussing how to explore a set of ordinal variables. The statistician suggest to plot a histogram instead of a bar graph because the histogram is more accurate than the bar graph. What do you think about his suggestion? (1 point)
2.4 The superintendent and her statistician are discussing how to explore a set of ordinal variables. The superintendent suggest to compute only the median as it is very likely that the mode will be capture in the computations. What should the statistician advice? (1 point)
2.5 The superintendent and her statistician are discussing how to explore a set of ratio variables, the superintendent suggest to explore only the mean and the standard deviation because these are the statistics that usually are presented in research journals. The statistician agrees with her. Are they correct? If not, what would you do?(1 point)
2.6 The superintendent and her statistician are discussing how to explore a set of ratio variables, they decided to plot a box-plot, a histogram, a bar graph, and a density function graph. What do you think about their decision? (1 point)
3. A group of students are playing a game that involves tossing a well-balanced dice to determine who wins in case two people tied. After tossing the dice ten times they surprisingly found the following distribution: 1112261166. One of the students claimed that the game has a cheap dice that is not well-balanced; thus they should get a new dice to be fair. Do you agree? Please justify your answer –Note no calculations of probabilities are needed.(5 points)
4. A group of math experts are interested in conducting a study that evaluates the effect of an educational math program among students attending elementary education (K-5, Kindergarten to fifth grade) in the state of Michigan. They designed an evaluation of their math program. They used a well know standardized math test and collected survey information about several personal, social and school factors. They designed a quasi-experimental study where they had two main groups: students who were exposed to their math program (experimental group) and students who were not included in the program (control group). They collected information before and after the implementation of the program. The information collected before will be referred as pre-test and the information collected after will be referred as post-test. For example, the math pretest score is the score of the standardized math test before the program was implemented; while the math post-test score is the score of the standardized math test after the program was implemented. Based on this information answer the following:
4.1 They claimed that the estimated math achievement mean before the implementation of the program was very similar between the control group and experimental group. They reported that thispopulation mean was 504.0023. What is the population they are referring? (1 point)
4.2 The research team statistician presented descriptive statistics of the pretest math score. The head of the research team notes that the sample mean of the control group is 504.5678 and the sample mean of experimental group is 503.7895. He concludes that it can safely be assumed that the two groups have similarpopulation means. Do you agree with him? Why?(2 points)
4.3 The head of the research team affirms that we can certainly assure that the mean of 504.0023 is the exact value for the parameter.
4.3.1 What is the parameter that he is referring?(1 point)
4.3.2 Would you agree with him? Justify your answer. (1 point)
4.3.3 The head of the research team insists that the exact value of the parameter is 504.0023, what additional information would you need to support or reject his claim?(1 point)
4.4 The statistician run a set of descriptive statistics for two continuous variables: Math pretest and student intelligenceiq. Table 1 shows this information. Using the information in the table answer the following:
4.4.1 What is the value for both variances? (1 point)
4.4.2 Does the statistician have enough information to tell if both distributions are close to a normal distribution? Explain your answer.(2 points)
4.4.3 Can the spread of the distributions be compared using the standard deviation? Why? (2 points)
4.4.4 Using the standard deviation and the mean the head of the research team concludes that both math and iq have very similar variation or spread. Is he correct? Why?(2 points)
4.4.5 The head of the research team is asking the statistician to tell him what the value of the population mean is for IQ. What should the statistician say?(2 points)
Table 1.
Descriptive statistics for math post test scores and student intelligence score
Math Post test IQ
Statistic 95%CI Statistic 95%CI
Mode 503.58 403.58
Mean 500 499.5 ; 501.24 400 399.5 ; 401.58
Median 507 407
Standard deviation 100 100
Variance
Kurtosis 0.354 0.245
Skewness 0.124 0.07
Minimum 150 150
Maximum 987 987
4.5 The research team is interested in comparing the mathematics posttest means of the control group and the experimental groupto make inferences to the population of students. Please provide step by step what you need to do to perform this estimation. Hint:No calculations are required but you need to be as comprehensive as possible.(3 points)
4.6 The head of the research teams long ago stop doing statistics and he is asking on of her statisticians to remind him how could they compare the math pretest and math posttest population means; pleasesuggest step by step how this comparison could be made. Hint:No calculations are required but you need to be as comprehensive as possible.(3 points)
4.7 The head of the research team found a report of an old study -Kids of Michigan- about math achievement among elementary students in Michigan. He found in the Kids of Michigan study that the estimated mean for math was 510.458. He is wondering if something could be done to confirm if this estimation is correct. The statistician gives him two alternatives:
4.7.1 Assuming that the math scores in the Kids of Michigan study and their study are equivalent; the statistician proposes to run a one sample Z-Test. Is the statistician correct? If so, what information does the statistician needs to perform this calculation?(2 points)
4.7.2 Assuming that he math score in Kids of Michigan study are NOT equivalent to the math scores in our study;the statistician proposes to run a one sample T-Test. Is the statistician correct? If so, what information does the statistician needs to perform this calculation?(2 points)
4.8 The research team design a sample using simple random sample procedures; however, when the head of the research team was reviewing the data collection process, he finds out that the Kalamazoo school district decided not to participate in the study. He argues that given that only Kalamazoo did not participated and they spent 4 million dollars in collecting data; there will not be any problems when making inferences to the population. What do you think? (3 points)
4.9 The research team also measured attitudes towards mathematics before and after the math program was implemented; while describing the scores of these two measurements they plotted Figure 1. Based on the this figure please answer the following:
4.9.1 Under what condition can it be assumed that the range of the scores is the same in both measurements of attitudes? (2 points)
4.9.2 What would be the range of the distribution of attitudes towards mathematics after the implementation?(2 points)
4.9.3 In what distribution would the mean be bigger than the median? Why?(2 points)
4.9.4 In what distribution would the median be bigger than the mean? Why?(2 points)
4.9.5 Approximately what would be the difference between the modes of attitudes towards mathematics before and after the implementation of the program?(2 points)
4.9.6 In order to explore the shape of the distribution what other information is needed?(2 points)
4.9.7 Can we have an idea of how would a boxplot look like for any of the distributions? Choose one alternative
a. No, SPSS or any other software is needed.
b. Yes, please draw both of them.
Figure 1: Distribution of attitudes towards mathematics before and after the implementation of the mathematics educational program.
4.10 Among the factors related to math achievement, the research team collected the number of hours per month that students spent studying mathematics, they displayed these hours in the following stem-leaf plot.
Based only on information provided in the graph, please answer:
4.10.1 The Head of the research team argues that the measurement scale of the number of hours per month is interval. Do you agree? Why? (2 point)
4.10.2 Looking at the graph the statistician says that we can calculate the median for the number of hours per month that students spent studying math. Can you calculateit?(2 point)
4.10.3 A graduate student argues that the research team could have saved money and time if they would not collected data on the hours of math study per month. He argues that this information is NOT relevant. Would you agree with him? Justify your answer.(2 point)
4.10.4 Outline a research questions that aims to explore the relationship between hours of study math during the month and mathematics achievement after the implementation of the program. (1point)
Part 2: This part is meant to be completed individually, however, running the analysis in SPSS could be done in small groups no larger than 4 students.
If you decide to work in groups to run the analysis please provide the following information.
Group member information for three students:
1. Name and id class:
2. Name and id class:
3. Name and id class:
4. Name and id class:
Once you are done with the analysis please work individually without exchanging any information and address the following questions (NOTE that any indication that there is other kind of collaboration in answering the questions would be subject to academic misconduct):
5. You will find in e learning a dataset named hds_midterm.sav containing information about vocabulary acquisition among pre-kindergarten students who attended two different pre- school programs: head start, other pre-school program, and not attending any pre-school program. Using the information below please generate a codebook for the dataset. You will have to present a codebook as your answer. As well as the syntax used. (6 points)
Variable Information
Variable Label
gender student gender
race student race
program treatment group
age age at beg of preschyr
fthrpres father inhousehold
reading amtmthrrds to child
momed mother’s education
rooms rooms/people in hsehold
famsize no cldrn/adults in hsehld
ppvt1 Peabody Pic Vocab Score beg of yr
ppvt2 Peabody Pic Vocab score end of yr
ses Social Class
Variable Values
Value Label
gender 1 male
2 female
race 1 white
2 black
program 1 Head Start
2 no preschool
3 other preschool
fthrpres 0 absent
1 present
reading 0 never
1 very infrequently
2 infrequently
3 once in a while
4 fairly often
5 every day
6. Perform a comparison on the vocabulary score at the end of the kindergarten (ppvt2) by race assuming that the sample is simple random sample and representative of the kindergarten population among Michigan students. Outline all your procedures from a research question to practical conclusion.(14 points)
7. Perform a comparison comparing the vocabulary scores at the beginning of the school year (ppvt1) and at the end of the school year (ppvt2). Assume that the sample is simple random sample and representative of the kindergarten population among Michigan students. Outline all your procedures from a research question to practical conclusion.(13 points)
8. Fully explore using adequate descriptive statistics and graphs one nominal variable, one ordinal variable and one interval variable. Please include a full interpretation as well.(14 points)
9. The population age for the kindergarten students according to the census was 49.75 months. Based on information collected in our data set what can you conclude? Show all your procedures used to address this question. (13 points)
Place your order now and save 15% by using the following discount code: welcome15 to enjoy this special discount, place your order within 2 weeks