Q T1.13. - The Practice of Statistics for AP

Question

A study among the Pima Indians of Arizona investigated the relationship between a mother’s diabetic status and the appearance of birth defects in her children. The results appear in the two-way table below. 

(a) Fill in the row and column totals in the margins of the table.

(b) Compute (in percentages) the conditional distributions of birth defects for each diabetic status.

(c) Display the conditional distributions in a graph. Don’t forget to label your graph completely.

(d) Comment on any clear associations you see.

Step-by-Step Solution

Answer

Part (a) 

Birth defects	Nondiabetic	Prediabetic	Diabetic	Total
None	754	362	38	1154
One or more	31	13	9	53
Total	785	375	47	1207

Part (b) 

Birth defects	Nondiabetic	Prediabetic	Diabetic	Total
None	65%	31%	3%	100%
One or more	58%	25%	17%	100%
Total	65%	31%	4%	100%

Part (c) 

Part (d) There is a non-diabetic relationship with no birth defects.

Part (a) Step 1: Given information

The table is given 

Birth defects	Nondiabetic	Prediabetic	Diabetic	Total
None	754	362	38
One or more	31	13	9
Total

Part (a) Step 2: Concept

Data analysis is the systematic application of statistical and/or logical tools to explain and show, condense and recap, and appraise data.

Part (a) Step 3: Explanation

The table is 

Birth defects	Nondiabetic	Prediabetic	Diabetic	Total
None	754	362	38	1154
One or more	31	13	9	53
Total	785	375	47	1207

Part (b) Step 1: Explanation

The table is 

Birth defects	Nondiabetic	Prediabetic	Diabetic	Total
None	65%	31%	3%	100%
One or more	58%	25%	17%	100%
Total	65%	31%	4%	100%

Part (c) Step 1: Explanation

The graph is 

Part (d) Step 1: Explanation

It is clear from the graph plot that there is no diabetic link with no birth abnormalities.