Stats 845 Assignment 1 - Review of Introductory Statistics

  1. (One-way ANOVA F test) Researchers studied the association between birth mother’s smoking habits andthe birth weights of their babies. A sample of size n = 11 subjects was selected from each of the four groups.

Group 1 – nonsmokers

Group 2 – smokers who smoked less that 1 pack per day

Group 3 – smokers who smoke more than 1 Pack but less than 2 packs per day

Group 4–smokers who smoke more than 2 packs per day.

The data is tabulated below:

Table: Birth weights (in grams) of infants of mothers (n = 11) in four smoking groups

nonsmokers / < 1pack / 1 pack to 2
packs / > 2 packs
3510 / 3444 / 2608 / 2232
3174 / 3111 / 2555 / 2331
3580 / 2890 / 3100 / 2200
3232 / 3002 / 1775 / 2121
3884 / 2995 / 2985 / 2001
3982 / 3101 / 2479 / 1566
4055 / 3400 / 2901 / 1676
3459 / 3764 / 2778 / 1783
3998 / 2997 / 2099 / 2002
3852 / 3031 / 2500 / 2118
3421 / 3120 / 2322 / 1882

Use the above data to construct an ANOVA table to determine if there is a significant difference in the average birth weight amongst the four groups. Illustrate your findings graphically

  1. (Chi-square test for independence) In the following study the investigator was interested in determining if the

Presence of Heart Disease was related to Systolic Blood pressure. The study

consisted of four groups of subjects with differing levels of Systolic Blood

pressure (<127, 127-146, 147-166, 167+). The data is tabulated below:

Coronary
Heart
Disease / Systolic Blood pressure (mm Hg)
<127127-146147-166167+
Present / 20 / 28 / 20 / 24
Absent / 388 / 527 / 204 / 118
Total / 408 / 555 / 224 / 142

Determine if there is a relationship between thePresence of Heart Disease andSystolic Blood pressure.

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  1. (Simple Linear Regression Model) In the following study a researcher was interested in whether infant mortality was related to the level of pollution in the city. For this purpose he collected the followingdata for n = 20 heavily populated localities. For each locality, an index (X) measuring the average daily level of pollution was determined along with the average infant mortality rate, (Y) over the past ten years. The data is tabulated below:
  1. Estimate the parameters of the least squares line.
  2. Determine 95% confidence limits for the parameters of the least squares line.
  3. Plot a graph of the data showing the least squares line.
  4. What conclusions would you make from this analysis?
  5. Predict the infant mortality rate in the city where the pollution index was 10.7. Compute 95 % prediction limits for this mortality rate

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