Reference no: EM132260226
Assignment - Solve these two questions by using STATA program and use very easy solutions
Question 1 - Storytelling and the use of language
A study of early childhood education asked kindergarten students to retell two fairy tales that had been read to them earlier in the week. The 10 children enrolled in the study included 5 high-progress readers and five low-progress readers. Each child told two stories. Story 1 had been read to them; Story 2 had been read and also illustrated with pictures. An expert listened to a recording of each child and assigned a score for certain uses of language. The data set Story.csv is on Blackboard and recorded in the table below. (Data provided by Susan Stadler, Purdue University)
|
Child
|
Progress
|
Story1
|
Story2
|
|
1
|
High
|
0.55
|
0.8
|
|
2
|
High
|
0.57
|
0.82
|
|
3
|
High
|
0.72
|
0.54
|
|
4
|
High
|
0.7
|
0.79
|
|
5
|
High
|
0.84
|
0.89
|
|
6
|
Low
|
0.4
|
0.77
|
|
7
|
Low
|
0.72
|
0.49
|
|
8
|
Low
|
0
|
0.66
|
|
9
|
Low
|
0.36
|
0.28
|
|
10
|
Low
|
0.55
|
0.38
|
We want to determine if children do a better job at retelling a story if the story that is read to them is illustrated rather than just read to them.
i. For the data given above, calculate the difference Story2 - Story1. Investigate whether the differences are normally distributed. What can you conclude?
ii. Use Stata to conduct a matched pairs t-test. State the hypotheses that you are testing, report the test statistic, the p-value and the conclusion to the test.
iii. State the hypotheses that you would want to test if you were to use the Sign Test to test the same claim.
iv. Compute the Sign Test statistic, K, by hand. (Include the appropriate table.) Calculate the p-value, and state your conclusion to the test.
v. Compute the Wilcoxon Signed-Rank test statistic, VW, by hand. (Include the appropriate table.) Use Stata to compute the p-value and report the value it produces. What do you conclude?
vi. Compare the conclusions to the three tests you have computed. Do you reach the same decision in each of them? How did the p-values compare?
Question 2 - Pollution Control
Two types of instruments for measuring the amount of sulfur monoxide in the atmosphere are being compared in an air-pollution experiment. The data set pollution.csv on Blackboard contains the readings of sulfur monoxide that were recorded by each of the instruments each day for a period of two weeks. The variables are day, instrA and instrB which contain respectively the day the reading was made and the level of sulfur monoxide recorded by instrument A and instrument B respectively. Investigate the data to determine if the data satisfies the appropriate assumptions, then use the appropriate test to determine whether the two instrument readings are the same. State the specific hypotheses that you are testing. Report the value of the test statistic, the p-value of the test, and the conclusion of the test. Provide the Stata output that you used to get the test statistic and p-value.
|
Day
|
InstrA
|
InstrB
|
|
1
|
0.96
|
0.87
|
|
2
|
0.82
|
0.74
|
|
3
|
0.75
|
0.63
|
|
4
|
0.61
|
0.55
|
|
5
|
0.89
|
0.76
|
|
6
|
0.64
|
0.7
|
|
7
|
0.81
|
0.69
|
|
8
|
0.68
|
0.57
|
|
9
|
0.65
|
0.53
|
|
10
|
0.84
|
0.88
|
|
11
|
0.59
|
0.51
|
|
12
|
0.94
|
0.79
|
|
13
|
0.91
|
0.84
|
|
14
|
0.77
|
0.63
|