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For the following pairs of assertions, indicate which do not comply with our rules for setting up hypotheses and why (the subscripts 1 and 2 differentiate between quantities for two different populations or samples). (a) Ho : M = 100, Ha : / > 100 OThese hypotheses comply with our rules. O Ho cannot include equality, so these hypotheses are not in compliance. OEach / is a statistic, so these hypotheses do not comply with our rules. OThe asserted value in Ho should not appear in Ha, so these hypotheses are not in compliance. (b) Ho : 0 = 20, Ha : 0 100 These hypotheses comply with our rules. O Ho cannot include equality, so these hypotheses are not in compliance. OEach / is a statistic, so these hypotheses do not comply with our rules. OThe asserted value in Ho should also appear in Ha, so these hypotheses are not in compliance.(e) Ho : ST = S2 , H. : S; # S These hypotheses comply with our rules. O Ho cannot include equality, so these hypotheses are not in compliance. OEach S is a statistic, so these hypotheses do not comply with our rules. OThe asserted value in Ho should not appear in Ha, so these hypotheses are not in compliance. (f) Ho : u = 120, Ha : / = 150 OThese hypotheses comply with our rules. O Ha cannot include equality, so these hypotheses are not in compliance. OEach / is a statistic, so these hypotheses do not comply with our rules. OIf A appears in Ho, then it should not appear in Ha, so these hypotheses are not in compliance. (9) Ho: - = 1, Ha : _ #1 02 OThese hypotheses comply with our rules. O Ho cannot include equality, so these hypotheses are not in compliance. OEach o is a statistic, so these hypotheses do not comply with our rules. OThe asserted value in Ho should not appear in Ha, so these hypotheses are not in compliance. (h) Ho : P1 - p2 = -0.1 , Ha : P1 - P2 5 or Ho : u =5 versus Ha : u 5. A type II error in this case involves deciding the water is safe when it isn't. This is a very serious error, so a test which ensures that this error is highly unlikely is desirable. We prefer that the most serious error be a type II error because it can be explicitly controlled. OOne should test Ho : M = 5 versus Ha : / 5. A type I error in this case involves deciding the water is safe when it isn't. This is a very serious error, so a test which ensures that this error is highly unlikely is desirable. We prefer that the most serious error be a type I error because it can be explicitly controlled.You may need to use the appropriate table in the Appendix of Tables to answer this question. The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let / denote the true average reflectometer reading for a new type of paint under consideration. A test of Ho : / = 20 versus H. : / > 20 will be based on a random sample of size n from a normal population distribution. What conclusion is appropriate in each of the following situations? (Round your P-values to three decimal places.) (a) n = 13, t = 3.3, a = 0.05 P - value = State the conclusion in the problem context. O Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. O Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. (b) n = 9, t = 1.7, a=0.01 P - value = State the conclusion in the problem context. O Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. O Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. (c) n = 28 , t = -0.4 P - value= State the conclusion in the problem context. O Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. O Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.You may need to use the appropriate table in the Appendix of Tables to answer this question. A common characterization of obese individuals is that their body mass index is at least 30 [BMI = weight/(height) ", where height is in meters and weight is in kilograms]. An article reported that in a sample of female workers, 266 had BMIs of less than 25, 158 had BMIs that were at least 25 but less than 30, and 123 had BMIs exceeding 30. Is there compelling evidence for concluding that more than 20% of the individuals in the sampled population are obese? (a) State the appropriate hypotheses with a significance level of 0.05. O Ho: p = 0.20; Ha: p 0.20 Ho: p = 0.20; Ha: p # 0.20 Calculate the test statistic. (Round your test statistic to two decimal places.) 2 = Determine the P-value. (Round your P-value to four decimal places.) P-value = What can you conclude? O Do not reject the null hypothesis. There is not sufficient evidence that more than 20% of the population of female workers is obese. O Reject the null hypothesis. There is not sufficient evidence that more than 20% of the population of female workers is obese. O Reject the null hypothesis. There is sufficient evidence that more than 20% of the population of female workers is obese. O Do not reject the null hypothesis. There is sufficient evidence that more than 20% of the population of female workers is obese. (b) Explain in the context of this scenario what constitutes type I error. O A type I error would be declaring that 20% or less of the population of female workers is obese, when in fact more than 20% are actually obese. O A type I error would be declaring that 20% or more of the population of female workers is obese, when in fact less than 20% are actually obese. O A type I error would be declaring that less than 20% of the population of female workers is obese, when in fact 20% or more are actually obese. O A type I error would be declaring that more than 20% of the population of female workers is obese, when in fact 20% or less are actually obese. Explain in the context of this scenario what constitutes type II error. O A type II error would be declaring that 20% or less of the population of female workers is obese, when in fact more than 20% are actually obese. O A type II error would be declaring that 20% or more of the population of female workers is obese, when in fact less than 20% are actually obese. O A type II error would be declaring that less than 20% of the population of female workers is obese, when in fact 20% or more are actually obese. O A type II error would be declaring that more than 20% of the population of female workers is obese, when in fact 20% or less are actually obese. (c) What is the probability of not concluding that more than 20% of the population is obese when the actual percentage of obese individuals is 24%? (Round your answer to four decimal places.) probability =[For the following pairs, indicate which do not comply wi'di the rules for setting up hypotheses, and explain why. [Select all that apply.) (a) H0: 1.: = 12, H3: :1 = 12 CI This pair complies. I] This pair does not comply because 3: is not a population characteristic. I] This pair does not comply because both hypotheses use an equal sign. I] This pair does not comply because the two hypotheses use different numbers. (b) He: p = 0.6, Ha: p :3 0.? C] This pair complies. C] This pair does not comply because p is not a population characteristic. C] This pair does not comply because both hypotheses use an equal sign. C] This pair does not comply because the two hypotheses use different numbers. (c) Ho: p = 120, He: p c 120 E] This pair complies. E] This pair does not comply because :1 is not a population characteristic. E] This pair does not comply because both hypotheses use an equal sign. E] This pair does not comply because the two hypotheses use different numbers. (d) H0: ,u = 124, Ha: ,u = 125 CI This pair complies. I] This pair does not comply because 3: is not a population characteristic. I] This pair does not comply because both hypotheses use an equal sign. I] This pair does not comply because the two hypotheses use different numbers. (e) Ho C] This pair complies. : = 0.2, Ha: a: 0.2 C] This pair does not comply because :3 is not a population characteristic. C] This pair does not comply because both hypotheses use an equal sign. C] This pair does not comply because the two hypotheses use different numbers