4. [1/7.5 Points] DETAILS PREVIOUS ANSWERS You may need to use the appropriate appendix table answer this question. On its municipal website, the city of Tulsa states that the rate it charges per 5 CCF of residential water is $21.62. How do the residential water rates of other U.S. public utilities compare to Tulsa's rate? The data shown below ($) contains the rate per 5 CCF of residential water for 42 randomly selected U.S. cities. 10.58 9.28 11.9 6.6 12.52 14.63 15.66 10.22 14.6 16.28 17.7 19.28 18.08 12.95 16.9 17.45 15.74 14.9 19.01 18.09 15 18.52 16.15 26.95 22.42 22.86 21.08 23.55 19.15 23.8 19.36 23.85 27.9 27.15 27.24 27.09 24.78 37.96 26.61 39.11 29.56 41.75 (a) Develop the hypotheses to test for evidence that the population mean rate per 5 CCF of residential water charged by U.S. public utilities differs from the $21.62 rate charged by Tulsa. Use the "Relations" tab and/or the "Greek" tab in the mathPad at the right of the screen if needed. Remember: Enter != for as needed. Ho 21.62 H: 21.62 (b) What is the test statistic for your hypothesis test in part (a)? (Round your answer to three decimal places.) -1.148 What is the p-value for your hypothesis test in part (a)? (Round your answer to four decimal places.) 0.2576 x (c) At a 0.05, can your null hypothesis be rejected? What is your conclusion? O Reject Ho. Conclude there is evidence that the mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa. Do not reject Ho. Conclude there is evidence that the mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa. O Do not reject H. Conclude there is evidence that the mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa. O Reject Ho. Conclude there is evidence that the mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa. (d) Repeat the preceding hypothesis test using the critical value approach. Restate the null and alternative hypotheses. Use the "Relations" tab and/or the "Greek" tab in the mathPad at the right of the screen if needed. Remember: Enter Ho -1.148 x H -1.148 Reenter the value of the test statistic. (Round your answer to three decimal places.) -1.148 x State the critical values for the rejection rule. Use a = 0.05. (Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.) test statistics-1.148 test statistic -1.148 for as needed. At a 0.05, what is your conclusion? O Reject H. Conclude there is evidence that the mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa. Do not reject H. Conclude there is evidence that the mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa. Do not reject Ho. Conclude there is evidence that the mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa. O Reject Ho. Conclude there is evidence that the mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa. 5. [1/3.5 Points] DETAILS PREVIOUS ANSWERS You may need to use the appropriate appendix table to answer this question. A study showed that 62% of supermarket shoppers believe supermarket brands to be as good as national name brands. To investigate whether this result applies to its own product, the manufacturer of a national name-brand ketchup asked a sample of shoppers whether they believed that supermarket ketchup was as good as the national brand ketchup. (a) Select the correct hypotheses to test for evidence that the percentage of supermarket shoppers who believe that the supermarket ketchup was as good as the national brand ketchup is less than 62%. Ho: P=0.62 H: p 0.62 Ho: p = 0.62 H: p > 0.62 Ho: p=0.62 H: p* 0.62 Ho: P = 0.62 H: p < 0.62 Ho: p < 0.62 H: p = 0.62 (b) Suppose for a sample of 100 shoppers, 49 stated that the supermarket brand was as good as the national brand. Find the value of the test statistic. (Round your answer to two decimal places.) -2.266 Find the p-value. (Round your answer to four decimal places.) p-value= 0.0117 (c) At a = 0.05, what is your conclusion? Reject H. There is sufficient evidence to conclude that the percentage of supermarket shoppers who believe that supermarket ketchup is as good as the national brand ketchup is less than 62%. O Do not reject Ho. There is not sufficient evidence to conclude that the percentage of supermarket shoppers who believe that supermarket ketchup is as good as the national brand ketchup is less than 62%. O Do not reject H. There is sufficient evidence to conclude that the percentage of supermarket shoppers who believe that supermarket ketchup is as good as the national brand ketchup is less than 62%. O Reject H. There is not sufficient evidence to conclude that the percentage of supermarket shoppers who believe that supermarket ketchup is as good as the national brand ketchup is less than 62%. (d) Should the national brand ketchup manufacturer be pleased with this conclusion? Explain. No, the national brand ketchup manufacturer should not be pleased with this conclusion. The results of the hypothesis test did not indicate that the percentage of shoppers who believe that supermarket ketchup is as good as the national brand ketchup was less than the overall percentage for all products. O Yes, the national brand ketchup manufacturer should be pleased with this conclusion. The results of the hypothesis test indicated that the percentage of shoppers who believe that supermarket ketchup is as good as the national brand ketchup was less than the overall percentage for all products. O No, the national brand ketchup manufacturer should not be pleased with this conclusion. The results of the hypothesis test indicated that the percentage of shoppers who believe that supermarket ketchup is as good as the national brand ketchup was less than the overall percentage for all products. Yes, the national brand ketchup manufacturer should be pleased with this conclusion. The results of the hypothesis test did not indicate that the percentage of shoppers who believe that supermarket ketchup is as good as the national brand ketchup was less than the overall percentage for all products. 6. [0/3.5 Points] DETAILS PREVIOUS ANSWERS You may need to use the appropriate appendix table to answer this question. Suppose in 2018, RAND Corporation researchers found that 77% of all individuals ages 66 to 69 are adequately prepared financially for retirement. Many financial planners have expressed concern that a smaller percentage of those in this age group who did not complete high school are adequately prepared financially for retirement. (a) Develop the hypotheses to test for evidence that the proportion those who are adequately prepared financially for retirement is smaller for people in the 66-69 age group who did not complete high school than it is for the population of 66-69 year old individuals. Use the "Relations" tab and/or the "Greek" tab in the mathPad at the right of the screen if needed. Remember: Enter != for + as needed. Ho H: 0.77 0.77 (b) Suppose a random sample of 300 people from the 66-69 age group who did not complete high school found 159 were not prepared financially for retirement. Find the value of the test statistic. (Round your answer to two decimal places.) -8.23 x Find the p-value. (Round your answer to four decimal places.) p-value = (c) At a 0.01, what is your conclusion? Reject Ho. Conclude there is not evidence that the population proportion of 66- to 69-year-old individuals who are adequately prepared financially for retirement is smaller for those who did not complete high school. Do not reject Ho. Conclude there is not evidence that the population proportion of 66- to 69-year-old individuals who are adequately prepared financially for retirement is smaller for those who did not complete high school. O Reject H. Conclude there is evidence that the population proportion of 66- to 69-year-old individuals who are adequately prepared financially for retirement is smaller for those who did not complete high school. O Do not reject H. Conclude there evidence that the population proportion of 66- to 69-year-old individuals who are adequately prepared financially for retirement is smaller for those who did not complete high school. Submit Answer 7. [-16 Points] DETAILS You may need to use the appropriate appendix table to answer this question. According to a research center, 6% of all merchandise sold in a particular country gets returned. A department store in a certain city sampled 80 items sold January and found that 12 of the items were returned. (a) Construct a point estimate of the proportion of items returned for the population f sales transactions at the store in the given city. (b) Construct a 95% confidence interval for the proportion f returns at the store in the given city. (Round your answers to four decimal places.) to (c) Is the proportion of returns at the store in the given city significantly different from the returns for the country as a whole? Provide statistical support for your answer. Select the hypotheses need to test for evidence that the proportion of returns at the store in the given city is significantly different from the returns for the country as a whole. HP 0.06 H: p 0.06 H: p 0.06 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value= At a = 0.01, what is your conclusion? Do not reject H. There sufficient evidence to conclude that the return rate for the store in the given city is different than the country's national return rate. O Reject H. There sufficient evidence conclude that the return rate for the store in the given city is different than the country's national return rate. Do not reject H. There is not sufficient evidence to conclude that the return rate for the store in the given city is different than the country's national return rate. Reject Ho. There is not sufficient evidence. conclude that the return rate for the store in the given city is different than the country's national return rate. Tutorial 8. [-/4 Points] DETAILS You may need to use the appropriate appendix table to answer this question. Vegetarians are much less common in the United States than in the rest of the world. Suppose in a 2018 survey of 12,000 people in the United States, VeganBits found 36 who are vegetarians. (a) Develop a point estimate of the proportion of people in the United States who are vegetarians. (b) Develop the hypotheses to test for evidence that the proportion of people in the United States who are vegetarians exceeds 0.002. Use the "Relations" tab and/or the "Greek" tab in the mathPad at the right of the screen if needed. Remember: Enter != for * as needed. Ho (c) Conduct your hypothesis test using a = 0.05. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = At a = 0.05, what is your conclusion? Do not reject Ho. Conclude there is not evidence that the population proportion of people in the United States who are vegetarians exceeds 0.002. Reject Ho. Conclude there is evidence that the population proportion of people in the United States who are vegetarians exceeds 0.002. O Reject Ho. Conclude there is not evidence that the population proportion of people in the United States who are vegetarians exceeds 0.002. Do not reject Ho. Conclude there is evidence that the population proportion of people in the United States who are vegetarians exceeds 0.002.