Question # 2 Determine (a) the x" test statistic, (b) the degrees of freedom, (c) the critical value using a = 0.05, and Outcome A B C DO (d) test the hypothesis at the a = 0.05 level of significance. Observed 107 107 94 92 Expected 100 100 100 100 Ho: PA = PB = PC = PD = 4 H: At least one of the proportions is different from the others. . . . (a) The test statistic is (Type an exact answer.)Question # 3 A manufacturer of colored candies states that 13% of the candies in a bag should be brown, 14% yellow, 13% red, 24% blue, 20% orange, and 16% green. A student randomly selected a bag of colored candies. He counted the number of candies of each color and obtained the results shown in the table. Test whether the bag of colored candies follows the distribution stated above at a = 0.05 level of significance. Using the level of significance a =0.05, test whether the color distribution is the same. Click here to view the table. Click here to view the table of critical values of the chi-square distribution, X Observed Distribution of Colors Colored Candies in a bag Color Brown Yellow Red Blue Orange Green Frequency 60 65 52 63 78 64 Compute the expected counts for each color. Claimed Proportion 0.13 0.14 0.13 0.24 0.20 0.16 Color Frequency Expected Count Brown 60 Yellow 65 Red 52 Print Done Blue 63 Orange 78 Green 64 (Round to two decimal places as needed.) What is the test statistic? XO = (Round to three decimal places as needed.) What is the range of P-values of the test? The range of P-values of the test isQuestion # 4 The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law. For example, the following distribution represents the first digits in 232 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer. Complete parts (a) through (c) below. Click the icon to view the tables. Distribution of First Digits - X Full data set Distribution of first digits (Benford's Law) Digit 1 2 3 4 5 Probability 0.301 0.176 0.125 0.097 Digit 0.079 6 8 9 Probability 0.067 0.058 0.051 0.046 First digits in allegedly fraudulent checks First digit 1 2 3 4 5 6 7 8 9 Frequency 42 What is the test statistic? 32 45 20 24 36 9 17 xo = (Round to three decimal places as needed.)Question # 6 A researcher wanted to determine whether certain accidents were uniformly distributed over the days of the week. The data show the day of the week for n = 293 randomly selected accidents. Is there reason to believe that the accident occurs with equal frequency with respect to the day of the week at the a = 0.05 level of significance? Click the icon to view the table. - X Distribution of accidents Compute the expected counts for day of the week. Day of the Day of the Week |Observed Count Expected Count Week Sunday Monday Tuesday Wednesday Thursday Friday Saturday Sunday 36 Frequency 36 40 27 37 41 52 60 Monday 40 Tuesday 27 Wednesday 37 41 Print Done Thursday Friday 52 Saturday 60 (Round to two decimal places as needed.) What is the test statistic? XO = (Round to three decimal places as needed.) What is the P-value of the test? P-value = (Round to three decimal places as needed.)