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- In a clinical study, a random sample of 540 participants agree to have their blood drawn, which is to be examined for the presence of antibodies against a certain contagious disease. It is found in 22% of the blood samples, which experimenters hope to extrapolate to the general population. From this random sample, 10 participants' blood samples are selected at random. If X is the number of samples out of the 10 who have these antibodies, what can we say about X? A. The sample size is not large enough for us to approximate X using a normal distribution B.The expected value of X is 22 C. X can be approximated using a normal distribution in lieu of a binomial distribution D. X has a sampling distribution that is normalIn a comparative study of two new drugs, A and B, 350 patients were treated with drug A, and 225 patients were treated with drug B. (The two treatment groups were randomly and independently chosen.) It was found that 241 patients were cured using drug A and 157 patients were cured using drug B. Let p1 be the proportion of the population of all patients who are cured using drug A, and let p2 be the proportion of the population of all patients who are cured using drug B. Find a 90% confidence interval for −p1p2 . Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your responses to at least three decimal places. (If necessary, consult a list of formulas.) What is the lower limit of the 90% confidence interval? What is the upper limit of the 90% confidence interval?A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same 10 cars, chosen at random. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in the table below. Car 1 2 3 4 5 6 7 8 9 10 Brand 1 0.54 0.62 0.37 0.42 0.58 0.50 0.53 0.64 0.53 0.40 Brand 2 0.39 0.33 0.33 0.33 0.28 0.46 0.29 0.55 0.45 0.37 Difference(Brand 1 - Brand 2) 0.15 0.29 0.04 0.09 0.30 0.04 0.24…
- Let p1 and p2 be the respective proportions of women with iron-deficiency anemia in each of two developing countries. A random sample of 1900 women from the first country yielded 513 women with iron-deficiency anemia, and an independently chosen, random sample of 1700 women from the second country yielded 515 women with iron-deficiency anemia. Can we conclude, at the 0.10 level of significance, that the proportion of women with anemia in the first country is less than the proportion of women with anemia in the second country? Perform a one-tailed test. Then complete the parts below.Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below. a. State the null hypothesis H0 and the alternative hypothesis H1. b. Find the values of the test statistic. c. FInd the p-value. d. Can we conclude that the proportion of women with anemia in the first country is less than the proportion of women with anemia in the second country?A potato chip company produces a large number of potato chip bags each day and wants to investigate whether a new packaging machine will lower the proportion of bags that are damaged. The company selected a random sample of 150 bags from the old machine and found that 15 percent of the bags were damaged, then selected a random sample of 200 bags from the new machine and found that 8 percent were damaged. Let pˆOp^O represent the sample proportion of bags packaged on the old machine that are damaged, pˆNp^N represent the sample proportion of bags packaged on the new machine that are damaged, pˆCp^C represent the combined proportion of damaged bags from both machines, and nOnO and nNnN represent the respective sample sizes for the old machine and new machine. Have the conditions for statistical inference for testing a difference in population proportions been met? No, the condition for independence has not been met, because random samples were not selected. A No, the…In a random sample of 320 cars driven at low altitudes, 50 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed. In an independent random sample of 135 cars driven at high altitudes, 17 of them exceeded the standard. Can you conclude that the proportion of high-altitude vehicles exceeding the standard is less than the proportion of low-altitude vehicles exceeding the standard? Let p1 denote the proportion of low-altitude vehicles exceeding the standard and p2 denote the proportion of high-altitude vehicles exceeding the standard. Use the =α0.10 level of significance and the P -value method with the TI-84 Plus calculator. please state all steps to the p method clearly!
- A study found that 1 out of 200 adult males have green eyes. If a random sample of 400 adult males is obtained, is the sampling of the sample proportion of males that have green eyes approximately normal? A. Yes, the sample size is greater than 10% of the population. B. Yes, the sample was randomly selected C. No, because np < 10 D. No, because nq < 10A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of 10 cars. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in the table below. Car 1 2 3 4 5 6 7 8 9 10 Brand 1 0.61 0.45 0.46 0.45 0.34 0.43 0.58 0.46 0.62 0.34 Brand 2 0.33 0.37 0.25 0.50 0.30 0.27 0.47 0.32 0.33 0.27 Difference(Brand 1 - Brand 2) 0.28 0.08 0.21 −0.05 0.04 0.16 0.11 0.14…A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of 10 cars. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in Table 1. Car Brand 1 Brand 2 Difference(Brand 1 - Brand 2) 1 0.362 0.293 0.069 2 0.363 0.335 0.028 3 0.220 0.168 0.052 4 0.364 0.297 0.067 5 0.399 0.395 0.004 6 0.351 0.338 0.013 7 0.386 0.377 0.009 8 0.276 0.251 0.025 9 0.206 0.228 -0.022 10 0.340 0.291 0.049 Table 1 Based on these data, can the consumer group conclude, at the 0.10…
- A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of 10 cars. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in the table below. Based on these data, can the consumer group conclude, at the 0.01 level of significance, that the mean tread wears of the brands differ? Answer this question by performing a hypothesis test regarding μd (which is μ with a letter "d" subscript), the population mean difference in tread wear for the two brands of tires. Assume that this population of differences (Brand 1…A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of 10 cars. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in Table 1. Car Brand 1 Brand 2 Difference(Brand 1 - Brand 2) 1 0.362 0.235 0.127 2 0.343 0.368 -0.025 3 0.203 0.230 -0.027 4 0.335 0.247 0.088 5 0.207 0.221 -0.014 6 0.344 0.332 0.012 7 0.354 0.285 0.069 8 0.385 0.382 0.003 9 0.273 0.236 0.037 10 0.376 0.328 0.048 Table 1 Based on these data, can the consumer group conclude, at the 0.05 level of…A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of 12 cars. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in Table 1. Car Brand 1 Brand 2 Difference(Brand 1 - Brand 2) 1 0.375 0.194 0.181 2 0.238 0.111 0.127 3 0.232 0.265 -0.033 4 0.201 0.184 0.017 5 0.366 0.203 0.163 6 0.206 0.106 0.100 7 0.254 0.311 -0.057 8 0.369 0.242 0.127 9 0.378 0.287 0.091 10 0.349 0.253 0.096 11 0.209 0.235 -0.026 12 0.352 0.188 0.164 Table 1 Based on these data, can the…
