A cognitive aptitude test consists of putting together a puzzle. Eleven people in group A took the test in a competitive setting (first and second to finish received a prize). Twelve people in group B took the test in a noncompetitive setting. The results follow (in minutes required to complete the puzzle). Group A 30 18 12 17 25 23 31 29 26 11 10   Group B 14 27 20 32 24 19 9 28 21 15 16 13 Use a 5% level of significance to test the claim that there is no difference in the distributions of time to complete the test. (a) What is the level of significance?   (b) Compute the sample test statistic. (Use 2 decimal places.) (c) Find the P-value of the sample test statistic. (Use 4 decimal places.)

Split the Bill?A recent study was conducted to compare the cost of restaurant meals when people pay individually versus splitting the bill as a group. In the experiment 48 subjects were randomly assigned to eight groups of six diners each. Half of the people were told they they would each be responsible for individual meals costs and the other half were told to split the cost equally among the six people at the table. The data in SplitBill includes the cost of what each person ordered (in Israeli shekels) and the payment method (Individual or Split). Use StatKey or other technology to construct a randomization distribution using these data to test whether there is sufficient evidence to conclude that the mean cost is lower when diners are paying individually than when they split the bill equally.   Here is the link to the data: http://www.lock5stat.com/datasets/SplitBill.txt

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To compare two elementary schools regarding teaching of reading skills, 12 sets of identical twins were used. In each case, one child was selected at random and sent to school A, and his or her twin was sent to school B. Near the end of fifth grade, an achievement test was given to each child. The results follow:  Twin Pair 1 2 3 4 5 6 School A 168 157 115 99 119 132 School B 123 142 110 110 120 122   Twin Pair 7 8 9 10 11 12 School A 120 121 132 145 138 88 School B 105 90 124 142 148 104   Suppose a sign test for matched pairs with a 8% level of significance is used to test the hypothesis that the schools have the same effectiveness in teaching reading skills against the alternate hypothesis that the schools have different levels of effectiveness in teaching reading skills. Let p denote portion of positive signs when the scores of school B are subtracted from the corresponding scores of school…