LAB SESSION 12

ANALYZING THE POPULATION VARIANCE

INTRODUCTION:  In this lab we will present the hypothesis test for the standard deviation for a normal population.  When sample data are skewed, just one outlier can greatly affect the standard deviation.  It is very important, especially when using small samples, that the sampled population be normal; otherwise the procedures are not reliable.  However, unlike the analysis for the mean you will not have convenient computer commands to help you.

To use Illustration 9-16 as an example of using Excel to aid in completion of the hypothesis test, let's assume the 12 samples tested yielded the following data:

165   172   180   189   181   173

167   192   212   169   198   171

Enter the data into Column A.

Determine the descriptive statistics by the following:

Choose:           Tools > Data Analysis > Descriptive Statistics

This gives you the following:

 165 Column1 172 180 Mean 180.75 189 Standard Error 4.152627865 181 Median 176.5 173 Mode #N/A 167 Standard Deviation 14.38512489 192 Sample Variance 206.9318182 212 Kurtosis 0.37412902 169 Skewness 1.005775368 198 Range 47 171 Minimum 165 Maximum 212 Sum 2169 Count 12 Confidence Level(95.0%) 9.139876928

From the table we see that n = 12, s = 14 and we calculate C2* = 21.56

To calculate the p-value, activate Cell B1.

Choose:           Insert > fx > Statistical > CHIDIST > OK

Enter:               C2*:    21.56

Df:     11 > OK

This gives you the value 0.0280.

Recall that the manufacturer claims “shelf life” is normally distributed.

Why is this important?

What decision should be made?

Does your conclusion match that for Illustration 9-16?

ASSIGNMENT:   Do Exercises 9.116 and 9.119 in your text.

Use the following data for 9.116

31.6   31.9   32.6   31.9   31.5   32.5   32.0   32.2   31.9  32.0

32.2   31.8   31.8   32.3   31.1   31.8   31.5   31.7   31.8  31.8