Question

7. The data processing department of an insurance company installed color video terminals to replace the monochrome units they had. The 95 operators trained to use the new machines averaged 7.2 hours before achieving satisfactory performance. The variance of the sample was 16.2 hours squared. The long experience of the operators with the old terminals indicated an average of 8.1 hours in the machines before their performance was satisfactory. At a significance level of 0.01, should the department supervisor conclude that it is easier to learn to operate the new terminals? Calculate the value of p. (All steps have to be manual)

Answer 1

given data are sample n=95

sample mean x =7.2 hour's

sample variance s^2= 16.2 hour's^2

population mean =8.1 hour's

null hypothesis H0 :- =8.1

alternative hypothesis Ha:- <8.1

level of significant =0.01

test statistic :-

t=

t= (7.2-8.1) /

= -0.9/0.4129

= -2.179

= -2.18

p value:-

in left tail at df=n-1=94

p (t <-2.18)= 0.0159

decision: -

pcal > p (i.e 0.0159> 0.01)

so fail to reject the null hypothesis H0

conclusion :-

at 1% significant level their is no sufficient evidence to support the claim that " it is easier to learn to operate the new terminals"