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Chapter9

# Chapter9 - 486 Chapter 9 Sampling Distributions ACTIVITY 9...

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- - : --- 486..-- Chapter 9 Sampling Distributions ACTIVITY 9A Young Women's Heights Materials: Several 3 " X 3" or 3 " X 5" Post-it Notes The height of young women varies approximately according to the N(64.5, 2.5) distribution. That is to say, the population of young women is normally distributed with mean p = 64.5 inches and standard deiiation u = 2.5 inches. The random variable measured is X = the height of a randomly selected young woman. In this activity you will use the TI-83KI-89 to sample from this distribution and then use Post-it Notes to construct a distribution of averages. 1. If we choose one woman at random, the heights we get in repeated choices follow the N(64.5,2.5) distribution. On your calculator, go into the StatisticsList Editor and clear Ll/listl. Simulate the heights of 100 ran- domly selected young women and store these heights in LIAistl as follows: Place your cursor at the top of LIRistl (on the list name, not below it). TI-83: Press IMATH], choose PRB, choose 6:randNorml. TI-89: Press m, choose 4:Probability, choose 6:.randNorm(. Complete the command: randNorm ( 64.5,2 .5,10 0 ) and press mi. 2. Plot a histogram of the 100 heights as follows. Deselect active functions in the Y = window, and turn off all STAT PLOTS. Set WINDOW dimen- sions to: X[57,72]2.5 and Y[-10,4515 to extend three standard deviations to either side of the mean, 64.5. Define PLOT 1 to be a histogram using the heights in Ll/listl. (You must set the Hist. Bucket Width to 2.5 in the TI-89 Plot Setup.) Press (on the TI-89 press an) to plot the histogram. Describe the approximate shape of your histogram. Is it fairly symmetric or clearly skewed? 3. Approximately how many heights should there be within 3u of the mean (i.e., between 57 and 72)? Use TRACE to count the number of heights within 3a. How many heights should there be within la of the mean? Within 2u of the mean? Again use TRACE to find these counts, and com- pare them with the numbers you would expect. 4. Use 1-Var Stats to find the mean, median, and standard deviation for your data. Compare f with the population mean p = 64.5. Compare the sample standard deviation s with a = 2.5. How do the mean and median for your 100 heights compare? Recall that the closer the mean and the median are, the more symmetric the distribution. 5. Define PLOT 2 to be a boqlot using LIAistl and then GRAPH again. The boxplot will be plotted above the histogram. Does the boxplot appear symmetric? How close is the median in the boxplot to the mean of the his-
ACTIVITY 9A Young Women's Heights (continued) togram? Based on the appearance of the histogram and the boxplot, and a comparison of the mean and median, would you say that the distribution is nonsymmetric, moderately symmetric, or very symmetric? 8. Repeat steps 1 to 5 two or three more times. Each time, record the mean z, median, and standard deviation s.

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