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The data below show the sugar content (as a percentage of weight) of several national brands of children’s and adults’ cereals. Create and interpret a 95% confidence interval for the difference in mean sugar content. Be sure to check the necessary assumptions and conditions Children's cereals: 40.3, 55, 45.7, 43.3, 50.3, 45.9, 53.5, 43,44.2,44,47.4,44,33.6,55.1,48.8,50.4,37.8,60.3,46.6 Adults' cereals: \(20,30.2,2.2,7.5,4.4,22.2,16.6,14.5,\) \(21.4,3.3,6.6,7.8,10.6,16.2,14.5,4.1,15.8,4.1,2.4,3.5,\) 8.5,10,1,4.4,1.3,8.1,4.7,18.4

Egyptians Some archaeologists theorize that ancient Egyptians interbred with several different immigrant populations over thousands of years. To see if there is any indication of changes in body structure that might have resulted, they measured 30 skulls of male Egyptians dated from 4000 B.c.E. and 30 others dated from 200 B.C.E. (A. Thomson and R. Randall-Maciver, Ancient Races of the Thebaid, Oxford: Oxford University Press, 1905\()\) a) Are these data appropriate for inference? Explain. b) Create a \(95 \%\) confidence interval for the difference in mean skull breadth between these two eras. c) Do these data provide evidence that the mean breadth of males' skulls changed over this period? Explain. d) Perform Tukey's test for the difference. Do your conclusions of part c change? \({ }^{*}\) e) Perform a rank sum test for the difference. Do your conclusions of part c change?

In Chapter 6 , Exercise 25 , we looked at collected samples of water from streams in the Adirondack Mountains to investigate the effects of acid rain. Researchers measured the pH (acidity) of the water and classified the streams with respect to the kind of substrate (type of rock over which they flow). A lower pH means the water is more acidic. Here is a boxplot of the \(\mathrm{pH}\) of the streams by substrate (limestone, mixed, or shale): Here are selected parts of a software analysis comparing the pH of streams with limestone and shale substrates: 2 -Sample \(t\) -Test of \(\mu_{1}-\mu_{2}\) Difference Between Means \(=0.735\) \(t\) -Statistic \(=16.30 \mathrm{w} / 133 \mathrm{df}\) \(\mathrm{p} \leq 0.0001\) a. State the null and alternative hypotheses for this test. b. From the information you have, do the assumptions and conditions appear to be met? c. What conclusion would you draw?

Researchers investigated how the size of a bowl affects how much ice cream people tend to scoop when serving themselves. \({ }^{12}\) At an "ice cream social," people were randomly given either a 17 -oz or a 34 -oz bowl (both large enough that they would not be filled to capacity). They were then invited to scoop as much ice cream as they liked. Did the bowl size change the selected portion size? Here are the summaries: 12Brian Wansink, Koert van Ittersum, and James E. Painter, "Ice Cream Illusions: Bowls, Spoons, and Self-Served Portion Sizes," Am. J. Prev. Med. 2006 . Test an appropriate hypothesis and state your conclusions. For assumptions and conditions that you cannot test, you may assume that they are sufficiently satisfied to proceed.

Is it a good idea to listen to music when studying for a big test? In a study conducted by some statistics students, 62 people were randomly assigned to listen to rap music, music by Mozart, or no music while attempting to memorize objects pictured on a page. They were then asked to list all the objects they could remember. Here are summary statistics for each group: a. Does it appear that it is better to study while listening to Mozart than to rap music? Test an appropriate hypothesis and state your conclusion. b. Create a \(90 \%\) confidence interval for the mean difference in memory score between students who study to Mozart and those who listen to no music at all. Interpret your interval.