Statistics Problems and Review

Types of Statistics Descriptive Used to measure a trait or characteristic without generalizing beyond the group: used to describe Inferential Used to make generalizations or inference from the smaller sample to a larger population

Histogram – Preoperative Prolactin Levels Problem #1

Normal Distribution Histogram

Runner #1 Mean = 4.00 Median = 3.85 Mode = 3.90 Runner #2 Mean = 4.04 Median = 4.00 Mode = 4.00 Runner #3 Mean = 3.9 Median = 3.9 Mode = 4.0 Which runner should the coach select for the last lap? Problem #2

Runner #1 Mean = 4.00 Median = 3.85 Mode = 3.90 Runner #3 Mean = 3.9 Median = 3.9 Mode = 4.0 Which runner should the coach select for the last lap? Problem #2

(a) Mean – 1 std dev includes 34.1% of the values. Values less than 1 std dev would be 50 – 34.1 or 15.9% times 300 in our sample = 47.7 Problem #3

(b) Mean + or – 1 std dev includes 68.2% of the values, 68.2% of 300 is Problem #3

(c) Mean outside of +2 std dev would be 2.3%, 2.3% of 300 is 7. Problem #3

$85,000 $45,000 $42,500 $43,000 $46,000 Mean = $52,300 Median = $45,000 Problem 4

Problem #5 Old MethodNew Method Wilcoxan Signed Rank Test Null: No difference Alter: Methods different Test statistic = 2.14, p 0.068

Problem #6 Factory A Factory B Factory C Total With Disease Without Disease Total

Problem #7 ParameterNew TreatmentControl Number7572 Gender (% male) 51%49% Age in years Mean (SD) 43 (8)44 (10)

Problem #8

Perfect Correlation r = 1.00 Slope = 1.00

Linear Correlation (r) Is There an Association? Measures linear relationship between 2 continuous variables. Interpreting r : Absolute Value Linear of r Relationship poor fair good.75 – 1.0very good

Problem #9 Mean weight loss: Walking = Cycling = 18.6 Swimming = -4 (gained) Statistical Test – One Way ANOVA Null hypothesis: No difference in weight loss among groups Alter: There is a difference in at least one group