4.A union representing the employees of a small industrial plant claims that it

Question

4.A union representing the employees of a small industrial plant claims that it takes an employee on an average at least 25 minutes to reach the closest local health clinic by cab; therefore, an industrial nurse should be hired. Management obtained a random sample of 49 one-way travel times to the clinic. The sample had a mean of 19.4 minutes with a standard deviation of 9.6 minutes. Does management have sufficient evidence to reject the union’s claim? = 0.1.

Ho:____________________

Ha:______________________

Test Statistics: _______________________

Decision Rule: _______________________

Decision: _____________________

Interpretation: ___________________

Explanation / Answer

Ho:>=25

Ha: :<25

Test Statistics: t=(xbar-32)/(s/sqrt(n))

=(19.4-25)/(9.6/sqrt(49))

=-4.08

Decision Rule: degree of freedom=n-1=49-1=48

Left tailed Critical t at 0.01 level is t=-2.4066

We reject H0 is calculated t<-2.4066 otherwise retain it

Decision: As calculated t<-2.4066, we reject the null hypothesis

Interpretation: We conclude that it takes an employee on an average lower than 25 minutes to reach the closest local health clinic by cab and so an industrial nurse need not be hired

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