Project #88916 - Assignement

 

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. 

 

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:   

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 this population mean was 504.0023. What is the population they are referring? 

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 similar population means. Do you agree with him? Why? 

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.

What is the parameter that he is referring? 

Would you agree with him? Justify your answer.

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? 

The statistician run a set of descriptive statistics for two continuous variables: Math pretest and student intelligence iq. Table 1 shows this information. Using the information in the table answer the following:

What is the value for both variances? 

Does the statistician have enough information to tell if both distributions are close to a normal distribution? Explain your answer. 

Can the spread of the distributions be compared using the standard deviation? Why? 

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? 

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? 

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

 

 

 

 

 

The research team is interested in comparing the mathematics posttest means of the control group and the experimental group to 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. 

 

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; please suggest step by step how this comparison could be made.  Hint: No calculations are required but you need to be as comprehensive as possible.

 

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:

 

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? 

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? 

 

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? 

 

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:

Under what condition can it be assumed that the range of the scores is the same in both measurements of attitudes?  

What would be the range of the distribution of attitudes towards mathematics after the implementation? 

In what distribution would the mean be bigger than the median? Why? 

In what distribution would the median be bigger than the mean? Why? 

Approximately what would be the difference between the modes of attitudes towards mathematics before and after the implementation of the program? 

In order to explore the shape of the distribution what other information is needed? 

Can we have an idea of how would a boxplot look like for any of the distributions? Choose one alternative 

No, SPSS or any other software is needed.

Yes, please draw both of them.

 SHAPE  \* MERGEFORMAT  

Figure 1: Distribution of attitudes towards mathematics before and after the implementation of the mathematics educational program. 

 

 

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:

 

The Head of the research team argues that the measurement scale of the number of hours per month is interval. Do you agree? Why? 

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 calculate it? 

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. 

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.  

 

Mathematics attitudes before implementation

 

Mathematics attitudes after implementation

 

 

 

Subject Mathematics
Due By (Pacific Time) 10/25/2015 12:00 pm
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