The production manager at a steel mill has reviewed the number of accidents that

Question

The production manager at a steel mill has reviewed the number of accidents that have occurred during the day, afternoon and night shifts over the past 5 years. The results for each shift are provided in the table below.

Day Afternoon Night

31, 18, 40,

22, 34, 42,

36 37 37

38 31 40

19 36 54

Test the hypothesis that there is no difference in the mean number of accidents occurring per year in the three shifts. Use a significance level of 0.05. Clearly show the steps of the hypothesis test that you use, and express your final conclusion using a clear English sentence.

Explanation / Answer

Here,

H0 :there is no difference in the mean number of accidents occurring per year in the three shifts.

H1 :there is difference in the mean number of accidents occurring per year in the three shifts.

For this the R-code is as ;

y=c(31,22,36,38,19,18,34,37,31,36,40,42,37,40,54)
x=rep(c(1,2,3),each=5)
d=data.frame(y,x)
a=aov(y~x,d)
summary(a)

And the output is as;

> summary(a)
Df Sum Sq Mean Sq F value Pr(>F)  
x 1 448.9 448.9 7.575 0.0165 *
Residuals 13 770.4 59.3
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Here p-value is less than 0.05 thus we reject null hypothesis and conclude that

There is difference in the mean number of accidents occurring per year in the three shifts.

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