# Statistics Problem Set: Hypothesis Testing Using Samples

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Problem 1:

A study by Hewitt Associates showed that 79% of companies offer employees flexible scheduling. Suppose a researcher believes that in accounting firms this figure is lower. The researcher randomly selects 415 accounting firms and through interviews determines that 303 of these firms have flexible scheduling. With a 1% level of significance, does the test show enough evidence to conclude that a significatly lower proportion of accounting firms offer employees flexible scheduling.

Problem 2:

A previous experience shows the variance of a given process to be 14. Researchers are testing to determine whether this value has changed. They gather the following dozen measurements of the process. Use these data and a significance level of .05 to test the null hypothesis about the variance. Assume the measurements are normally distributed.

52 44 51 58 48 49

38 49 50 42 55 51

Problem 3:

Highway engineers in Ohio are painting white stripes on a highway. The stripes are supposed to be approximately 10 feet long. However, because of the machine, the operator, and the motion of the vehicle carrying the equipment, considerable variation occurs among the stripe lengths. Engineers claim that the variance of stripes is not more than 16 inches. Use the sample lengths given here from 12 measured stripes to test the variance claim. Assume stripe length is normally distributed. Let the significance level = .05

Stripe Lengths in Feet

10.3 9.4 9.8 10.1

9.2 10.4 10.7 9.9

9.3 9.8 10.5 10.4.

#### Solution Preview

Problem 1:

Ho: p>=0.79

Ha: p<0.79.

This is one tailed t test.

The degree of freedom is 415-1=414, at 0.01 significance level, the critical value is -2.335.

p=303/415=0.73

The test value t=(0.73-0.79)/(sqrt(0.79*(1-0.79)/415)=-3.001

Since ...

#### Solution Summary

The solution discusses hypothesis testing using samples in the statistic problem set.