Exam 12: Tests With Qualitative Data

Find the area to the right of 23.337 under the chi-square distribution with 12 degrees of freedom.

The number of visits to a certain web site were counted each day of a particular week. The results are given in the following table. Day Number of Visits Sunday 146 Monday 114 Tuesday 120 Wednesday 115 Thursday 110 Friday 155 Saturday 130 Test the hypothesis that the web site visits are equally likely to occur on any day of the week. Use the level of significance.

Find the $\alpha = 0.01$ critical value for the chi-square statistic with 13 degrees of freedom.

For the given table of observed frequencies, perform a test for independence, using the α = 0.01 level of significance. 1 2 3 69 64 67 91 98 88 42 84 86

For the given table of observed frequencies: 1 2 3 60 61 53 87 90 81 41 94 82 i). Compute the row totals, the column totals, and the grand total. ii). Construct the corresponding table of expected values. iii). Compute the value of the chi-square test statistic. iv). Perform a test for independence, using the $\alpha = 0.05$ level of significance.

A psychology instructor gave a five-question true-false quiz to her class of 193 students. The results were as follows. Number Correct 0 1 2 3 4 5 Observed 6 26 58 59 25 19 The instructor thinks that the students may have answered the questions by guessing, so that the probability that any given answer is correct is 0.5. Under the null hypothesis, the number of correct answers has a binomial distribution with 5 trials and success probability 0.5. Perform a chi-square test of this hypothesis. Can you reject H₀ at the $\alpha$ =0.01 level?