Statistics 2480 Practice Problems 1. People with diabetes must monitor and contr

Question

Statistics 2480 Practice Problems 1. People with diabetes must monitor and control their blood glucose level. The goal is to maintain fasting plasma glucose between about 90 and 130 milligrams per deciliter. Here are the fasting plasma glucose levels of two groups of diabetics: A. Group A was enrolled in a diabetes control clas, five moriths after the end of the class 78 95 96 103 112 134 141 145 147 148 153 158 172 172 200 255 271 359 B. Group B was provided with one-on-one instruction on diabetes control. 128 128 158 159 160 163 164 188 195 198 220 221 223 226 227 283 a. Compute the five number summaries for the two groups of data. b. Does there appear to be a difference in the distribution of fasting plasma glucose between the two groups? Justify your answer. c. Explain the concepts of bias and confounding in the cntext of this example. 2. Why is randomization an important component of experimental design. 3. For the data in Problem (1) above, would it be correct to use the Empirical Rule to describe the data? Why or why not?

Explanation / Answer

a.

R code:

> A=c(78,95,96,103,112,134,141,145,147,148,153,158,172,172,200,255,271,359)
> B=c(128,128,158,159,160,163,164,188,195,198,220,221,223,226,227,283)

> summary(A)
Min. 1st Qu. Median Mean 3rd Qu. Max.
78.0 117.5 147.5 163.3 172.0 359.0
> summary(B)
Min. 1st Qu. Median Mean 3rd Qu. Max.
128.0 159.8 191.5 190.1 221.5 283.0

b. There is a difference in fasting plasma glucose between two groups.

Group B is approximately symmetric, as, median = mean.

Group A the distribution is right skewed . that means positively skewed. as median < mean

2. Because it is generally extremely difficult for experimenters to eliminate bias using only their expert judgment, the use of randomization in experiments is common practice. In a randomized experimental design, objects or individuals are randomly assigned (by chance) to an experimental group. Using randomization is the most reliable method of creating homogeneous treatment groups, without involving any potential biases or judgments.

3. The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean. The empirical rulecan be broken down into three parts: 68% of data falls within the first standard deviation from the mean. 95% fall within two standard deviations.

group A cannot be described by emperical rule as it is nor symmetric

group B can be described by emperical rule.as it is symmetric

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