Figure 3.6 Sets of 1000 sample means (a) Assume that two of the distributions show results from 1000 random samples , while two others show distributions from a sampling method that is biased . Which two dotplots appear to show samples produced using a biased sampling method ? Explain your reasoning . Pick one of the distributions that you listed as biased and describe a sampling method that might produce this bias . (b) For the two distributions that appear to show results from random samples , suppose that one comes from 1000 samples of size n=100 and one comes from 1000 samples of size n=500 . Which distribution goes with which sample size ? Explain 3.26 Mix It Up for Better Learning In preparing for a test on a set of material , is it better to study one topic at a time or to study topics mixed together? In one study, " a sample of fourth graders were taught four equations . Half of the children learned by studying repeated examples of one equation at a time , while the other half studied mixed problem sets that included examples of all four types of calculations grouped together. A day later, all the students were given a test on the material . The students in the mixed practice group had an average grade of 77, while the students in the one -at-a-time group had an average grade of 38. What is the best estimate for the difference in the average grade between fourth -grade students who study mixed problems and those who study each equation independently ? Give notation (as a difference with a minus sign ) for the quantity we are trying to estimate , notation for the quantity that gives the best estimate , and the value of the best estimate . Be sure to clearly define any parameters in the context of this situation . 3.28 Hollywood Movies Data 2.7 introduces the dataset HollywoodMovies2011, which contains information on all the 136 movies that came out of Hollywood in 2011 45 One of the variables is the budget (in millions of dollars ) to make the movie . Figure 3.8 shows two boxplots . One represents the budget data for one random sample of size n=30. The other represents the values in a sampling distribution of 1000 means of budget data from samples of size 30