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Assignment Submission For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer. Assignment Scoring Your last submission is used for your score. 1. [-/2 Points] MendStat15 14.R.001.S. To see whether a new floor polish A was superior to those produced by four competitors, B, C, D, and E, a manufacturer asked a sample of 100 housekeepers to view five identical patches of flooring that had received the five polishes. Each indicated the patch that he or she considered superior in appearance, with the results shown in the table. Polish ABCDE Frequency 28 18 16 23 15 LA USE SALT Do these data present sufficient evidence to indicate a preference for one or more of the polished patches of floor over the others? (Use a = 0.05.) State the null and alternative hypotheses. Ho: At least one p; is different from 0. Ha: p1 = p2 = p3 = p4 = p5 = 0 Ho: P1 = p2 = p3 = p4 = p5 = 0 Ha: At least one pi is different from 0. C Ho: p1 = p2 = p3 = p4 = p5 = Ha: At least one pi is different from UC Ho: P1 = p2 = p3 = p4 = P5 = 1 Ha: At least one pi is different from 1. C Ho: At least one pi is different from U - Ha: p1 = p2 = p3 = p4 = ps = 1 5 Find the test statistic. X2 = What can be said about the p-value? p-value 0.100 State your conclusion. Since the p-value is greater than 0.05, Ho is rejected. There is insufficient evidence to conclude that there is a difference in the preference for the five floor polishes. Since the p- value is less than 0.05, Ho is rejected. There is sufficient evidence to conclude that there is a difference in the preference for the five floor polishes. C Since the p-value is greater than 0.05, Ho is not rejected. There is insufficient evidence to conclude that there is a difference in the preference for the five floor polishes. Since the p-value is less than 0.05, Ho is not rejected. There is sufficient evidence to conclude that there is a difference in the preference for the five floor polishes. If one were to reject the hypothesis of no preference for this experiment, would this imply that polish A is superior to the others? Yes, since the conclusion would be that all of the values of the p; are significantly different from which implies that polish A is greater than U -Yes, since the conclusion would be that at least one of the values of the pi was significantly different from and polish A has the highest frequency. . Yes, since the conclusion would be that at least one of the values of the pi was significantly different from U - which implies that polish A is greater than U - No, since the conclusion would be that all of the values of the pi are significantly different from UI but this does not imply that polish A is necessarily greater than No, since the conclusion would be that at least one of the values of the pi was significantly different from but this does not imply that polish A is necessarily greater than U Can you suggest a better way of conducting the experiment? You may need to use the appropriate appendix table to answer this question.2. [-/2 Points] MendStat15 14.R.002. To investigate the effect of general hospital experience on the attitudes of physicians toward Medicare patients, a random sample of 50 physicians who had just completed 4 weeks of service in a general hospital were surveyed, generating the data in the table. Concern After Concern Before High Low Total Low 26 5 31 High 10 9 19 Chi-Square Test Chi-Square DF P-Value Pearson 5.702 0.017 Likelihood Ratio 5.617 1 0.018 Do the data provide sufficient evidence to indicate an association between the level of concern after general hospital experience and the level of concern before? (Use a = 0.05. Use the exact values found in the MINITAB output.) State the null and alternative hypotheses. Ho: Level of concern after is independent of level of concern before. Ha: Level of concern after is dependent of level of concern before. Ho: Level of concern after is independent of level of concern before. Ha: Level of concern after is linearly related to level of concern before. C Ho: Level of concern after is linearly related to level of concern before. Ha: Level of concern after is independent of level of concern before. Ho: The physicians and Medicare patients have the same concerns. Ha: The physicians and Medicare patients have different concerns. "Ho: Level of concern after is dependent of level of concern before. Ha: Level of concern after is independent of level of concern before. State the test statistic. X2 = State the p-value. p-value = 1 State the conclusion. Ho is rejected. There is insufficient evidence to indicate the level of concern after is dependent on the level of concern before. Ho is rejected. There is sufficient evidence to indicate the level of concern after is dependent on the level of concern before. Ho is not rejected. There is insufficient evidence to indicate the level of concern after is dependent on thelevel of concern before. Ho IS not rejected. There is sufcrent ev1dence to mdlcate the level of concern after is dependent on the level of concern before. Do the data suggest a change in "concern" after the general hospital experience? If so, describe the nature of the change. in A large proportion of physicians appear to change their level of concern from high to low after general hospital experience. r A small proportion of physicians appear to change their level of concern from high to low after general hospital experience. r A large proportion of physicians appear to change their level of concern 'om low to high after general hospital experience. r A small proportion of physicians appear to change their level of concern from low to high after general hospital experience. r The physicians' level of concern stayed the same after general hospital experience. You may need to use the appropriate appendix table or technology to answer this question. 3. [12 Points] MendStatlS 14.R.003.S. Two biology instructors set out to evaluate the effects of discovery-based teaching compared to the standard lecture-based teaching approach in the laboratory. The discovery-based approach asked questions rather than providing directions, and used small group reports to decide the best way to proceed in reaching the laboratory objective. At the end of the course, students provided evaluations as is given in the following table. Positive Negative Group Evaluations Evaluations Total Discovery 38 10 48 Control 33 15 48 IE USE SALT (a) Is there a signicant difference in the proportion of positive responses for each of the teaching methods? Use a: = 0.05. State the null and alternative hypotheses. (II. H0: Evaluation and teaching approach are independent. Ha: Evaluation and teaching approach are linearly related. r' Ho: Evaluation and teaching approach are linearly related. Ha: Evaluation and teaching approach are independent. r Ho: The proportion of positive evaluations is not the same for the two teaching approaches. . . . . . . 1\" H..: The proportion of posrtive evaluations is the same for the two teaching approaches. Ho: The numbers of positive and negative evaluations are equal. Ha: The numbers of positive and negative evaluations are not equal. Ho: The proportion of positive evaluations is the same for the two teaching approaches. Ha: The proportion of positive evaluations is not the same for the two teaching approaches. Find the test statistic. (Round your answer to two decimal places.) X2 = Find the rejection region. (Round your answer to two decimal places.) X2 > State your conclusion. C Ho is rejected. There is sufficient evidence to conclude that there is a difference in the proportion of positive responses for each teaching method. Ho is rejected. There is insufficient evidence to conclude that there is a difference in the proportion of positive responses for each teaching method. Ho is not rejected. There is insufficient evidence to conclude that there is a difference in the proportion of positive responses for each teaching method." Ho is not rejected. There is sufficient evidence to conclude that there is a difference in the proportion of positive responses for each teaching method. If there is a significant difference, how would you describe this difference? There is a significantly higher proportion of positive evaluations in the control group than in the discovery group. There is no significant difference. There is a significantly higher proportion of positive evaluations in the discovery group than in the control group. There is a significantly higher proportion of negative evaluations in the control group than in the discovery group. There is a significantly higher proportion of negative evaluations in the discovery group than in the control group. (b) What is the approximate p-value for the test in part (a)? p-value 0.100 You may need to use the appropriate appendix table to answer this question. 4. [-/2 Points] MendStat15 14.R.007.S. How confident are you that the food you purchase is safe to eat? This question was asked in a poll. The data that follow reflect the results of the responses to this poll. Very Somewhat Not Too Not at All Confident Confident Confident Confident Total Men 211 242 69 6 528 Women 130 307 74 17 528 Total 341 549 143 23 1,056LA USE SALT (a) Is there sufficient evidence to conclude that there are significant differences in responses between men and women at the a = 0.05 level of significance? State the null and alternative hypotheses. C Ho: Poll responses and gender are independent. Ha: Poll responses and gender are dependent. Ho: Poll responses and gender are independent. Ha: Poll responses and gender are linearly related. Ho: The responses for men and women are equal. Ha: The responses for men and women are not equal. Ho: Poll responses and gender are linearly related. Ha: Poll responses and gender are independent. Ho: Poll responses for men and women are dependent. Ha: Poll responses for men and women are independent. Find the test statistic. (Round your answer to two decimal places.) X2 = Find the rejection region. (Round your answer to two decimal places.) X 2 > State your conclusion. Ho is rejected. There is insufficient evidence to indicate significant differences among responses between men and women. Ho is not rejected. There is sufficient evidence to indicate significant differences among responses between men and women. Ho is rejected. There is sufficient evidence to indicate significant differences among responses between men and women. Ho is not rejected. There is insufficient evidence to indicate significant differences among responses between men and women. (b What can be said about the p-value for the test? C p-value 0.100 You may need to use the appropriate appendix table to answer this question. 5. [-/2 Points] MendStat15 14.R.008. No matter the make or model of a new vehicle, white and silver/gray continue to make the top five or six colors across all categories. The top six colors and their percentage of the market share for compact/sports cars are shown in the following table.Color Silver Black Gray Blue Red White Percent 14 21 17 09 11 21 To verify the figures, a random sample consisting of 250 compact/sports cars was taken and the color of the vehicles recorded. The sample provided the following counts for the categories given above: 39, 54, 38, 19, 22, 52, respectively. (a) Is any category missing in the classification? Yes No How many vehicles belong to that category? (If there are no categories missing, enter NONE.) (b) Is there sufficient evidence to indicate that our percentages of the colors for compact/sports cars differ from those given? (Use a = 0.05.) State the null and alternative hypotheses. C Ho: At least one p; is different from Ha: P1 = p2 = p3 = p4 = ps = p6 = p7 = C Ho: p1 = 0.14; p2 = 0.21; p3 = 0.17; p4 = 0.09; ps = 0.11; p6 = 0.21; p7 = 0.07 Ha: No value of pi is the same as its specified value. Ho: p1 = p2 = p3 = p4 = p5 = p6 = p7 = Ha: At least one pi is different fromHo: p1 = 0.14; p2 = 0.21; p3 = 0.17; p4 = 0.09; ps = 0.11; p6 = 0.21; p7 = 0.07 Ha: At least one pi is different from the specified value. Ho: At least one pi is different from the specified value. Ha: P1 = 0.14; p2 = 0.21; p3 = 0.17; p4 = 0.09; p5 = 0.11; p6 = 0.21; p7 = 0.07 Find the test statistic. (Round your answer to two decimal places.) X2 = 1 Find the approximate p-value for the test. p-value 0.100 State your conclusion. Since the p-value is less than 0.05, Ho is rejected. There is sufficient evidence to suggest a difference from the given percentages. Since the p-value is greater than 0.05, Ho is rejected. There is insufficient evidence to suggest a difference from the given percentages. C Since the p-value is less than 0.05, Ho is not rejected. There is sufficient evidence to suggest a difference from the given percentages. Since the p-value is greater than 0.05, Ho is not rejected. There is insufficient evidence to suggest a difference from the given percentages. You may need to use the appropriate appendix table or technology to answer this question. 6. [-/2 Points] MendStat15 14.R.010. The prevalence and patterns of knee injuries among women collegiate rugby players were investigated using a sample questionnaire, to which 49 rugby clubs responded. A total of 86 knee injuries were classified by type as well as the position (forward or back) of the player. Type of Knee Injury Meniscal MCL ACL Patella PCL Position Tear Tear Tear Dislocation Tear Forward 13 16 7 2 Back 12 11 14 2 Chi-Square Test for Association: Position, Injury Rows: Position Columns: Injury Meniscal Tear MCL Tear ACL Tear Patella PCL Tear All Forward 13 16 2 12.50 13.50 10.50 4.50 2.00 43Back 12 11 14 4 2 12.50 2.00 43 13.50 10.50 4.50 All 25 27 21 9 4 86 Cell Contents Count Expected count Chi-Square Test Chi-Square DF P-Value Pearson 3.410 4 0.492 Likelihood Ratio 3.461 4 0.484 4 cell(s) with expected counts less than 5. (a) Use the MINITAB printout to determine whether there is a difference in the distribution of injury types for rugby backs and forwards. (Use a = 0.05. Use the exact values found in the MINITAB output.) State the null and alternative hypothesis. C Ho: Injury type and player position do no exhibit a linear association. Ha: Injury type and player position exhibit a linear association. Ho: Injury type and player position exhibit a linear association. Ha: Injury type and player position do not exhibit a linear association. Ho: Injury type and player position are independent. Ha: Injury type and player position are dependent. Ho: Injury type and player position are dependent. Ha: Injury type and player position exhibit a do not linear association. Ho: Injury type and player position are dependent. Ha: Injury type and player position are independent. Report the appropriate p-value. State your conclusions. Ho is not rejected. There is sufficient evidence to indicate injury type and player position are dependent. Ho is not rejected. There is insufficient evidence to indicate injury type and player position are dependent. Ho is rejected. There is insufficient evidence to indicate injury type and player position are dependent. Ho is rejected. There is sufficient evidence to indicate injury type and player position are dependent.Have any of the assumptions necessary for the chi-square test been violated? What effect will this have on the magnitude of the test statistic? (II. Yes, the assumption of multinomial experiment conditions being met has been violated. This . . . If" . . . has no effect on the magnitude of the test statistic. Yes, the assumption of multmomial experiment conditions being met has been violated. This increases the size of the test . . f' . . . statistic. Yes, the assumption of expected cell counts exceeding ve has been Violated. . . . . . If\" . This increases the Size of the test statistic. Yes, the assumption of expected cell counts exceeding ve has been violated. This decreases the size of the test statistic. F No assumptions have been violated. (b) The investigators report a significant difference in the proportion of MCL tears for the two positions (P State your conclusion. Ho is rejected. There is sufficient evidence to indicate that susceptibility to colds is affected by the number of relationships you have. Ho is not rejected. There is sufficient evidence to indicate that susceptibility to colds is affected by the number of relationships you have. Ho is not rejected. There is insufficient evidence to indicate that susceptibility to colds is affected by the number of relationships you have. Ho is rejected. There is insufficient evidence to indicate that susceptibility to colds is affected by the number of relationships you have. (b Based on the results of part (a), describe the nature of the relationship between the two categorical variables: cold incidence and number of social relationships. Do your observations agree with the author's conclusions? As the number of relationships increases, it appears that the susceptibility to a cold seems to which with the author's conclusions. You may need to use the appropriate appendix table to answer this question. 8. [-/2 Points] MendStat15 14.R.013.S. A criminologist studying criminal offenders who have a record of one or more arrests is interested in knowing whether the educational achievement level of the offender influences the frequency of arrests. He has classified his data using four educational level classifications.. A: completed 6th grade or less B: completed 7th, 8th, or 9th grade . . C: completed 10th, 11th, or 12th grade D: education beyond 12th grade The contingency table shows the number of offenders in each educational category, along with the number of times they have been arrested. Educational Achievement Number of Arrests B C D 54 41 44 31 14 24 17 21 3 or More 8 7 11 11 LA USE SALT Do the data present sufficient evidence to indicate that the number of arrests is dependent on the educational achievement of a criminal offender? Test using a = 0.05. State the null and alternative hypotheses. C Ho: Number of arrests and educational achievement are independent. Ha: Number of arrests and educational achievement are dependent. Ho: Number of arrests and educational achievement are independent. Ha: Number of arrests and educational achievement are linearly related. Ho: Number of arrests and educational achievement are dependent. Ha: Number of arrests and educational achievement are independent. Ho: The numbers of people in each educational achievement category are equal. Ha: The numbers of people in each educational achievement category are not equal. Ho: Number of arrests and educational achievement are linearly related. Ha: Number of arrests and educational achievement are independent. Find the test statistic. (Round your answer to two decimal places.) X2 = 1 Find the rejection region (Round your answer to two decimal places.) X2 > State your conclusion. C Ho is rejected. There is sufficient evidence to conclude that the number of arrests is dependent on the educational achievement of the criminal offender. Ho is not rejected. There is insufficient evidence to conclude that the number of arrests is dependent on the educational achievement of the criminal offender. Ho is rejected. There is insufficient evidence to conclude that the number of arrests is dependent on the educational achievement of the criminal offender. Ho is not rejected. There is sufficient evidence to conclude that the number of arrests is dependent on the educational achievement of the criminal offender.You may need to use the appropriate appendix table to answer this question. 9. [-/2 Points] MendStat15 14.R.501.XP. A freeway with four lanes in each direction was studied to see whether drivers prefer to drive on the inside lanes. A total of 1,000 automobiles were observed during heavy early-morning traffic, and the number of cars in each lane was recorded. Lane 1 2 3 4 Observed Count 297 272 237 194 Do the data present sufficient evidence to indicate that some lanes are preferred over others? Test using a = 0.05. State the null and alternative hypotheses. C Ho: At least one pi is different from Ha: P1 = p2 = p3 = p4 = 1 Ho: At least one p; is different from 0. Ha: p1 = p2 = p3 = p4 = 0 Ho: p1 = p2 = p3 = p4 = 1 Ha: At least one pi is different from 1. C Ho: p1 = p2 = p3 = p4 = 0 Ha: At least one pi is different from 0. Ho: P1 = p2 = p3 = p4 = 1 Ha: At least one pi is different fromA Find the test statistic. X2 = Find the rejection region. (Round your answer to three decimal places.) X2 > State your conclusion. Ho is not rejected. There is sufficient evidence to indicate a difference in preference for the four lanes. Ho is not rejected. There is insufficient evidence to indicate a difference in preference for the four lanes. Ho is rejected. There is insufficient evidence to indicate a difference in preference for the four lanes. Ho is rejected. There is sufficient evidence to indicate a difference in preference for the four lanes. If there are any differences, discuss the nature of the differences. There a difference in preference for the four lanes. They seem to You may need to use the appropriate appendix table or technology to answer this question. 10. [-/2 Points] MendStat15 14.R.006.S. A team of researchers investigated the level of preparation of economics graduate students for their teaching-related duties for students at "top-tier" and those at "second-tier" schools. The responses to the question "Are you satisfied with the level of preparation you have had for your teaching-related duties?" follow. Top-Tier Second-Tier I am very satisfied 87 198 I am somewhat satisfied 103 170 I am unsatisfied 23 30 Total 213 398 In USE SALT (a) Is there a significant difference in the responses to the question between students at "top-tier" schools compared to those at "second-tier" schools? (Use a = 0.05.) State the null and alternative hypotheses.Ho: Satisfaction and tier of school are independent. Ha: Satisfaction and tier of school are dependent. " Ho: Satisfaction and tier of school are linearly related. Ha: Satisfaction and tier of school are dependent. Ho: Satisfaction and tier of school are independent. Ha: Satisfaction and tier of school are linearly related. Ho: Satisfaction and tier of school are equal. Ha: Satisfaction and tier of school are not equal. Ho: Satisfaction and tier of school are dependent. Ha: Satisfaction and tier of school are independent. Find the test statistic. (Round your answer to two decimal places.) X2 = 1 Find the rejection region. (Round your answer to two decimal places.) X2 > State your conclusion. C Ho is rejected. There is sufficient evidence to conclude that there is a significant difference in the responses to the question between students at the two types of schools. Ho is not rejected. There is sufficient evidence to conclude that there is a significant difference in the responses to the question between students at the two types of schools. Ho is rejected. There is insufficient evidence to conclude that there is a significant difference in the responses to the question between students at the two types of schools. " Ho is not rejected. There is insufficient evidence to conclude that there is a significant difference in the responses to the question between students at the two types of schools. (b) If significant, describe the nature of the differences in response for graduate students at "top-tier" versus "second-tier" schools. If you graduate at a "top-tier" school, it appears that you are more likely to be unsatisfied. C If you graduate at a "top-tier" school, it appears that you are more likely to be very satisfied. If you graduate at a "second-tier" school, it appears that you are more likely to be very satisfied. If you graduate at a "second-tier" school, it appears that you are more likely to be unsatisfied. There are no significant differences. You may need to use the appropriate appendix table to answer this