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

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Prolactin (ng/mL)

Histogram – Preoperative Prolactin Levels

Problem #1

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Normal Distribution Histogram

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sNormal 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 204.6.

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 = $52,300Median = $45,000

Problem 4

Problem #5Old Method New Method

25 27

43 44

37 39

26 24

27 30

55 55

47 51

34 36

58 59

32 33

Wilcoxan Signed Rank Test

Null: No difference

Alter: Methods different

Test statistic = 2.14, p 0.068

Problem #6Factory A

Factory B

Factory C

Total

With Disease

47 23 17 87

Without

Disease

212 287 125 624

Total 259 310 142 711

Problem #7Parameter New Treatment Control

Number 75 72

Gender

(% male)

51% 49%

Age in years

Mean (SD)

43 (8) 44 (10)

Problem #8

Perfect Correlation

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Linear Correlation (r)Is There an Association? Measures linear relationship between 2

continuous variables. Interpreting r :

Absolute Value Linearof r Relationship0 - .25 poor.25 - .50 fair.50 - .75 good.75 – 1.0 very good

Problem #9 Mean weight loss:

Walking = 17.09 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