# Inference

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The Human Resources Director of Wayjacks Inc. has administered a dexterity test to job

applicants for a period of several years. She assumes that the times required to complete the task are distributed with a mean of 10.8 minutes. The Director would like to know if applicants who have completed a vocational course tend to complete the task faster than the norm. For a sample of 16 applicants with such a course, she observed the average time of 10.2 minutes and standard deviation of 1.25 minutes to complete the task.

a. Set up appropriate hypotheses, give the p-value and report your conclusions.

b. Based on the result in (a) should she reject the null hypothesis at a=0.025? Explain.

c. What assumption(s) must you make in order that your answers are valid?

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##### Solution Summary

The Human Resources Director of Wayjacks Inc. has administered a dexterity test to job

applicants for a period of several years. She assumes that the times required to complete the task are distributed with a mean of 10.8 minutes. The Director would like to know if applicants who have completed a vocational course tend to complete the task faster than the norm. For a sample of 16 applicants with such a course, she observed the average time of 10.2 minutes and standard deviation of 1.25 minutes to complete the task.

a. Set up appropriate hypotheses, give the p-value and report your conclusions.

b. Based on the result in (a) should she reject the null hypothesis at a=0.025? Explain.

c. What assumption(s) must you make in order that your answers are valid?

##### Solution Preview

muo = 10.8 min

<br>n = 16

<br><X> = 10.2 min

<br>sd = 1.25 m

<br>

<br>a.)

<br>Null hypothesis Ho: mu <= muo

<br>Alternative hypothesis H1: <X> > muo

<br>

<br>Because,

<br>mu = <X> + z*sd/sqrt(n) <= muo

<br>z <= ...

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