Assig n ment 8

You’re a fourth-grade teacher, and you’ve saved extensive records of all your students for the past five years. Assume that your students are a sample of all fourth-graders in your state. For each of the following questions, state what test to use, how you would set up the data and the Ho/Ha if applicable. Please use full sentences.

1. What’s the major problem with your assumption?

2. You’re wondering if the distribution of grades was roughly Normal. How would you check this?

3. You have a nagging idea that shorter students tend to have better grades; maybe you could roughly predict a new student’s final grade by their height? And how accurate might that prediction be?

4. 4th-graders in the US take a standardized test for math. The national average score is 237. Did your state outperform the national average?

5. December holidays always seem such a distraction to 4th graders. Are December grades significantly worse than their October grades? If so, by how much?

6. You read in a magazine that, at this age, girls often have better grades in math than the boys. Is it significant?

7. In spite of that article, a fellow teacher feels that more of the boys pass math than the girls. Hmm, how would you test it?

8. Maybe the girls’ scores vary more than the boys’?

9. Redheads are rumored to have fiery tempers. Is there any significant difference in grades between blondes, brunettes, and redheads?

10. Do more redheads fail math than students with other hair colors?

Part 2

1. A company reports that the results of a phone survey indicate 80% of Americans prefer their product, with only a 3% margin of error. Do you trust this report? What problems aren’t included in a margin of error? Why are phone surveys still so common?
2. 
   
   This scatterplot of students’ heights looks really strong. What’s wrong with it?
   
   Women
   60 61 62 62 63 64 64 65 65 65 65 67 67 67 68 70
   
   Men
   63 67 67 67 68 70 70 71 72 72 73 74 74 75 77 79
   
3. 
   A student took a convenience sample of people at the local gym, asking age and weight. Using the regression equation of Weight=-1.16*Age + 214, the student predicted that a 10 year old would weigh 202.5 lbs. What’s going on here?
   
   Age
   22 24 28 30 33 35 39 42 43 49 51 55 56 62 67
   
   Weight
   130 165 180 185 250 180 175 170 170 160 160 155 155 138 100
   
4. 
   
   A convenience sample of height data was taken, and a two-sample t-test performed, with the following result. Is the difference between men’s and women’s heights of practical significance? How can this happen? What can you do to check for this?
   
   t-Test: Two-Sample Assuming Unequal Variances
   
   
   Men Women
   
   Mean
   69.58426966
   69.08427
   Variance
   0.722931563
   0.722932
   Observations
   89
   89
   Hypothesized Mean Difference
   0
   df
   176
   t Stat
   3.922847422
   P(T<=t) one-tail
   0.000062649
   t Critical one-tail
   1.653557436
   P(T<=t) two-tail
   0.000125298
   t Critical two-tail
   1.973534347
5. A fourth-grade teacher takes the math scores of the 10 tallest and 10 shortest students in the class, and performs a two-sample t-test on the data. The p-value is significant at alpha=0.05, and the teacher concludes that taller students are better at math. What are the problems with this conclusion?

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