(c) The solution to the IVP is given by: OA OB. 1 Y(0)= 17/20 -21 + 7/1 y(t) = = 1 12 1 6 5t
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Amish State Oil claims their gasoline additive increases fuel economy. Miles per gallon (MPG) for 15 identical vehicles were obtained and results are listed below in column one. These vehicles were given the gasoline additive and the MPG results are listed in column two. Find p and state your conclusion whether Amish State Oil’s claim is true, using a= 0.05.Persons having Raynaud's syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an experiment to study the extent of this impairment, each subject immersed a forefinger in water and the resulting heat output (cal/cm2/min) was measured. For m = 9 subjects with the syndrome, the average heat output was x = 0.61, and for n = 9 nonsufferers, the average output was 2.09. Let ?1 and ?2 denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal with ?1 = 0.3 and ?2 = 0.5. (a) Consider testing H0: ?1 − ?2 = −1.0 versus Ha: ?1 − ?2 < −1.0 at level 0.01. Describe in words what Ha says, and then carry out the test. Ha says that the average heat output for sufferers is the same as that of non-sufferers.Ha says that the average heat output for sufferers is less than 1 cal/cm2/min below that of non-sufferers. Ha says that the average heat output for sufferers is more…
- A veterinarian wishes to test dogs colorblindness. She puts dog food in 3 different color bowls and expects the results to be uniform. She samples 150 dogs and find the following observation. Color Green bowl 59 Blue bowl 44 Red bowl 47 Test the veterinarian’s claim at α = .10A dietitian wishes to see if a person’s cholesterol level will change if the diet is supplemented by a certain mineral. Six randomly selected subjects were pretested, and then they took the mineral supplement for a 6-week period. The results are shown in the table. (Cholesterol level is measured in milligrams per deciliter.) Can it be concluded that the cholesterol level has been changed at α = 0.10? Assume the variable is approximately normally distributed. Subject 1 2 3 4 5 6 Before (x1) 210 235 208 190 172 244 After (x2) 190 170 210 188 173 288 Required Steps: Step 1: Label all given information. Step 2:State the null and alternative hypothesis and identify the claim. Step 3:Verify that the conditions are met to perform the test. Step 4:Sketch the normal distribution and find the critical regions. Step 5:Compute the test statistic. Step 6:Make a decision Step 7:Summarize the results.A researcher has boiled her hypothesis test down to the following information.H0H0: μ=40μ=40, HaHa: μ>40μ>40, α=0.08α=0.08¯x=40.719x¯=40.719, s=5.8914s=5.8914, n=21n=21Find the p-value.
- Starting with x0 - 1.5, yo 1.2, the values x3 and y3 obtained using the pair formulae /+-y.. Y... -x -1 n=0,1,2 are (a) x3 = 1.562050, y3 = 1.322875 (b) x3 = 1.322875, y3 = 1.562050 (c) x3 = 1.526050, y3 1.322875 (e) x3 = 1.233875, y3 1.562050Persons having Raynaud's syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an experiment to study the extent of this impairment, each subject immersed a forefinger in water and the resulting heat output (cal/cm?/min) was measured. For m = 9 subjects with the syndrome, the average heat output was x = 0.62, and for n = 9 nonsufferers, the average output was 2.06. Let u, and uz denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal with o, = 0.1 and oz = 0.5. vA, says tnal ule a y---- Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) P-value = What is the probability of a type II error when the actual difference between u, and uz is u - uz = -1.1? (Round your answer to four decimal places.) Assuming that m = n, what sample sizes are required to ensure that 8 = 0.1 when u - uz…Persons having Raynaud's syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an experiment to study the extent of this impairment, each subject immersed a forefinger in water and the resulting heat output (cal/cm2/min) was measured. For m = 9 subjects with the syndrome, the average heat output was x = 0.63, and for n = 9 nonsufferers, the average output was 2.07. Let ₁ and ₂ denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal with ₁ = 0.1 and ₂ = 0.5. (a) Consider testing Ho: H₁ H₂ = -1.0 versus H₂: H₁ H₂ < -1.0 at level 0.01. Describe in words what H₂ says, and then carry out the test. OH says that the average heat output for sufferers is less than 1 cal/cm²/min below that of non-sufferers. ⒸH₂ says that the average heat output for sufferers is more than 1 cal/cm2/min below that of non-sufferers. OH says that the average heat output for sufferers is…
- A researcher has boiled her hypothesis test down to the following information. Ho: μ = 42, Ha: μ> 42, a = 0.09 x = 43.4386, s = 4.5039, n = 16 Find the p-value.Persons having Raynaud's syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an experiment to study the extent of this impairment, each subject immersed a forefinger in water and the resulting heat output (cal/cm?/min) was measured. For m = 9 subjects with the syndrome, the average heat output was x = 0.62, and for n = 9 nonsufferers, the average output was 2.06. Let u, and u, denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal with o, = 0.1 and o, = 0.5 What is the probability of a type II error vhen the actual difference between u, and uz is u, - uz = -1.1? (Round your answer to four decimal places.) Assuming that m = n, what sample sizes are required to ensure that B = 0.1 when u1 - H2 = -1.1? (Round your answer up to the nearest whole number.)A medical researcher says that less than 86% of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of 400 adults in that country, 84% think that healthy children should be required to be vaccinated. At a=0.10, is there enough evidence to support the researcher's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H, and H Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) O A. The percentage of adults in the country who think that healthy children should be required to be vaccinated is not % O B. Less than % of adults in the country think that healthy children should be required to be vaccinated. O C. More than % of adults in the country think that healthy children should be required to be vaccinated. O D. % of adults in the country think that healthy children should be required to be…
