Statistical Methods for Psychology

see that just as the central limit theorem predicted, the distribution is approximately nor-

mal, the mean is again at m550, and the standard deviation has been reduced to approxi-

mately.

You can get a better idea of the difference in the normality of the sampling distribution

when n 5 5 and n 5 30 by looking at Figure 7.2c. This figure presents Q-Q plots for the

two sampling distributions, and you can see that although the distribution for n 5 5 is not

very far from normal, the distribution with n 5 30 is even closer to normal.

28.87> 130 =5.27

182 Chapter 7 Hypothesis Tests Applied to Means

5.0010.015.020.025.030.035.040.045.050.055.060.065.070.075.080.085.090.0

Mean of 5

Frequency

0

100

200

300

400

500

Std. Dev = 12.93

Mean = 49.5

N = 5000.00

Figure 7.2a Sampling distribution of the mean when n 5 5

Figure 7.2b Sampling distribution of the mean when n 5 30

Mean of 30 observations

32.034.036.038.040.042.044.046.048.050.052.054.056.058.060.062.064.066.068.070.0

Frequency

1000

800

600

400

200

0

Std. Dev = 5.24

Mean = 50.1

N = 5000.00