# B describe and outline the design of this experiment

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(b) Describe and outline the design of this experiment. (c) It is efficient to have each taster rate fries from all treatments. How will you use randomization in presenting fries to the tasters? Questions on sampling distribution: 3.81 Effect of sample size on the sampling distribution. You are planning a study and are considering taking an SRS of either 200 or 400 observations. Explain how the sampling distribution would differ for these two scenarios. 3.82 What’s wrong? State what is wrong in each of the following scenarios. (a) A sampling distribution describes the distribution of some characteristic in a population. (b) A statistic will have a large amount of bias whenever it has high variability. (c) The variability of a statistic based on a small sample from a population will be the same as the variability of a large sample from the same population. 3.84 Bias and variability. Figure 3.15 (on page 222 ) shows histograms of four sampling distributions of statistics intended to estimate the same parameter. Label each distribution relative to the others as high or low bias and as high or low variability.
Exercise Questions: Chapter 3 FIGURE 3.15 Determine which of these sampling distributions displays high or low bias and high or low variability, for Exercise 3.84 3.95 Toss a coin. Coin tossing can illustrate the idea of a sampling distribution. The population is all outcomes (heads or tails) we would get if we tossed a coin forever. The parameter p is the proportion of heads in this population. We suspect that p is close to 0.5. That is, we think the coin will show about one-half heads in the long run. The sample is the outcomes of 20 tosses, and the statistic is the proportion of heads in these 20 tosses (count of heads divided by 20). (a) Toss a coin 20 times and record the value of (b) Repeat this sampling process 9 more times. Make a stemplot of the 10 values of You are constructing the sampling distribution of . Is the center of this distribution close to 0.5? (Ten repetitions give only a crude approximation to the sampling distribution. If possible, pool your work with that of other students to obtain several hundred repetitions and make a histogram of the values of .) . . .