So to see how often the boat was sent out with too

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So, to see how often the boat was sent out with too much weight, we need to know about the distribution of the average weight of 47 passengers from different boats (samples). Think about a distribution of sample mean weights from different random samples of 47 passengers, selected from the population of adult Americans. (e) Where do you think the distribution of sample means will be centered? (f) Do you think the distribution of sample means would have more variability, less variability, or the same variability as weights of individual people? Explain your answer. (g) Do you think the probability of having the average weight exceed 159.574 pounds is larger or smaller than the probability of the weight of any one passenger exceeding 159.574 pounds? To investigate this probability, we will generate random samples from a hypothetical population of adults’ weights. Open the WeightPopulations.xls data file and pretend each column is a different population of 20,000 adult tourists, each with a population mean weight ( P ) of 167 lbs and a population standard deviation ( V ) of 35 lbs. x Copy the data in the first column ( pop1 ) to the clipboard and then open the Sampling from Finite Population applet: Press Clear , Click inside the Paste population data box, and paste the data from the clipboard. Press Use Data . (h) Describe the shape, mean ( P ) and standard deviation ( V ) of this population distribution (shown the histogram below the window).
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Chance/Rossman, 2015 ISCAM III Investigation 2.4 152 x Check the Show Sampling Options box. Keep the Number of Samples at 1 and specify the Sample Size to be 47 and press the Draw Samples button. The distribution of weights for this random sample of 47 passengers from this population is displayed in blue and in the Most Recent Sample graph. (i) Describe the shape, center, and variability of this distribution. How does this sample distribution compare to the population distribution? Shape: Mean: Standard deviation: Comparison (samples vs. population): Notice that the mean of this sample ( ) has been added to the graph in the lower right Statistic graph. (j) Press Draw Samples again. Did you obtain the same sample of 47 weights? Did you obtain the same sample mean? Do either of the two sample means generated thus far equal the population mean? (k) Continue to press Draw Samples 8 more times (for 10 samples total), and notice the variability in the resulting sample means from sample to sample. Is a pattern beginning to emerge in the Statistic distribution graph? (l) Now set the Number of Samples to 990 (for 1000 total) and press Draw Samples . Describe the shape, center, and variability of the distribution of the sample means (lower right). How do these compare to the population distribution? [ Hints : Note the change in scaling. You can check the Population scale box to rescale back to the original population scaling and add the location of the population mean.] Which one of these features has changed the most, and how has it changed?
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