Question

152 400 6. One of the authors collected data from a class to see whether humans made selections, as a random mumber generator would. Each of 38 students has to pick an integer from one to five. The data are summarized in the table. Integer Times Chosen One Two Three Four Five 3 5 14 11 A true random mumber generator would create roughly equal nuimbers of all five integers. Perform a goodness-of-fit analysis to test humans are not like random number generators. Use a significance level a 0.05, and assume the data were from a random sample of students. 7. Is the die fair? You suspect that a die has been changed so that the outcomes of a roll, the mumbers 1 to 6, are not equally likely. You toss the die 600 times and obtain the following result. Outcome Count 2 3 4 5 6 87 80 125 117 100 91

Answer 1

Null hypothesis: There is no significant difference between the observed and the expected value.

Alternative Hypothesis HA: There is significant difference between the observed and the expected value.

alpha=0.05

Times chosen Oi Ei Oi-Ei 7.6 7.6 Integer One Two Three Four Five TOTAL MEAN 7.6 7.6 7.6 -4.6 -2.6 6.4 3.4 -2.6 (Oi-Ei)^2 21.16 6.76 40.96 11.56 6.76 Chi square (Oi-Ei)^2/Ei 2.784210526 0.889473684 5.389473684 1.521052632 0.889473684 11.47368421 5 38 7.6

Test statistic= 11.47

degrees pf freedom= 5-1=4

The P-Value is .02176. The result is significant at p < .05.

Decision: REJECT NULL HYPOTHESIS H0.

Conclusion: We have sufficient evidence to conclude that there is significant difference between the observed and the expected value.