Find the p-value.

Students use many kinds of criteria when selecting courses. "Teacher who is a very easy grader" is often one criterion. Three teachers are scheduled to teach statistics next semester. A sample of previous grade distributions for these three teachers is shown here. Professor Grades #1 #2 #3 A 11 13 25 B 14 28 25 C 35 28 13 Other 25 40 21 (a) At the 0.01 level of significance, is there sufficient evidence to conclude "The distribution of grades is not the same for all three professors?" (i) Find the test statistic. (Give your answer correct to two decimal places.) (ii) Find the p-value. (Give your answer bounds exactly.) < p < (iii) State the appropriate conclusion. Fail to reject H0. The distribution of grades is the same for all professors at the 0.01 level of significance. Fail to reject H0. The distribution of grades is not the same for all professors at the 0.01 level of significance. Reject H0. The distribution of grades is the same for all professors at the 0.01 level of significance. Reject H0. The distribution of grades is not the same for all professors at the 0.01 level of significance. (b) Which professor is the easiest grader? Professor #1 Professor #2 Professor #3 There is no evidence that one is easier than the others. Q. 2 Skittles Original Fruit bite-size candies are multicolored candies in a bag, and you can "Taste the Rainbow" with their five colors and flavors: green, lime; purple, grape; yellow, lemon; orange, orange; and red, strawberry. Unlike some of the other multicolored candies available, Skittles claims that their five colors are equally likely. In an attempt to reject this claim, a 4-oz bag of Skittles was purchased and the colors counted. Does this sample contradict Skittle's claim at the .05 level? Red Orange Yellow Green Purple 27 16 20 20 17 (a) Find the test statistic. (Give your answer correct to two decimal places.) (ii) Find the p-value. (Give your answer bounds exactly.) < p < (b) State the appropriate conclusion. Reject the null hypothesis, there is significant evidence to contradict Skittle's claim. Fail to reject the null hypothesis, there is not significant evidence to contradict Skittle's claim. Reject the null hypothesis, there is not significant evidence to contradict Skittle's claim. Fail to reject the null hypothesis, there is significant evidence to contradict Skittle's claim. Q. 3 Nursing Magazine reported results of a survey of more than 1800 nurses across the country concerning job satisfaction and retention. Nurses from magnet hospitals (hospitals that successfully attract and retain nurses) describe the staffing situation in their units, in the first table. A survey of 490 nurses from non-magnet hospitals gave the responses to the staffing situation in the second table. Do the data indicate that the nurses from the nonmagnet hospitals have a different distribution of opinions? Use α = .05. Staffing Situation Percent 1. Desperately short of help-patient care has suffered 12.6 2. Short, but patient care hasn't suffered 31.1 3. Adequate 32.8 4. More than adequate 12.3 5. Excellent 11.2 Staffing Situation 1 2 3 4 5 Number 153 138 115 49 35 (a) Find the test statistic. (Give your answer correct to two decimal places.) (ii) Find the p-value. (Give your answer bounds exactly.) < p < Q.4 A manufacturer of floor polish conducted a consumer-preference experiment to determine which of five different floor polishes was the most appealing in appearance. A sample of 100 consumers viewed five patches of flooring that had each received one of the five polishes. Each consumer indicated the patch he or she preferred. The lighting and background were approximately the same for all patches. The results are given below. Solve the following using the p-value approach and solve using the classical approach. Polish A B C D E Total Frequency 29 15 16 21 19 100 (a) State the hypothesis for "no preference" in statistical terminology. H0: P(A) ≠ P(B) ≠ P(C) ≠ P(D) ≠ P(E) H0: P(A) + P(B) + P(C) + P(D) + P(E) = 1 H0: P(x) = P(y) for some x and y H0: P(A) = P(B) = P(C) = P(D) = P(E) = 0.2 (c) Complete the hypothesis test using α = 0.10. (i) Find the test statistic. (Give your answer correct to two decimal places.) (ii) Find the p-value. (Give your answer bounds exactly.) < p < (iii) State the appropriate conclusion. Reject H0. There is significant evidence of a consumer preference. Do not reject H0. There is no evidence of a consumer preference. Q. 5 The proportions of defective parts produced by two machines were compared, and the following data were collected. Determine a 98% confidence interval for p1 - p2. (Give your answers correct to three decimal places.) Machine 1: n = 159; number of defective parts = 15 Machine 2: n = 159; number of defective parts = 4 Lower Limit Upper Limit