Answer to Question #239750 in Statistics and Probability for Joy

Question

The following are number of words per minute typef by 4 secretaried on 4 different typewriter models(ROYAL,IBM,UNDERWOOD,OLIVETRI)

Secretary

Kim ROYAL78..OLIVETRI 77

Doug ROYAL 57...OLIVETRI 60

Rhonda ROYAL 69...OLIVETRI83

Kevin ROYAL 71...OLEVITRI 67

KIM IBM 62...UNDERWOOD 71

DOUG IBM 49..UNDERWOOD 62

Rhonda IBM 78..UNDERWOOD 72

KEVIN IBM 66..UNDERWOOD 59

USE 0.05 LEVEL OF SIGNIFICANCE TO TEST THE HYPOTHESIS

a. The secretaries type with equal speed.

b. Different typewriters have no effect typing speed.

Answer 1

a)

running anova

Response: t1$speed

Df Sum Sq Mean Sq F value Pr(>F)

t1$sec 3 790.19 263.396 6.9967 0.005632 **

Residuals 12 451.75 37.646  

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

we see that p <.05 so we reject the null so secretary type with different speeds

b)

Analysis of Variance Table

Response: t1$speed

Df Sum Sq Mean Sq F value Pr(>F)

t1$typ 3 143.69 47.896 0.5233 0.6744

Residuals 12 1098.25 91.521

we see that p >.05 so we fail to reject the null so typewriter has no effect on typing speed