We are testing an effect of a potion that claimed to improve injured people's injuries with 80% of chance. The potion is given to 20 injured people and we observed the number "P" of people who improved. The hypothesis is Но: р %3D 0.8 vs. Н;;р<0.8 Use the rejection region RR = {y<12}
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- It is believed that a sweetener called xylitol helps prevent ear infections. In a randomized experiment, 165 children took a placebo and 68 of them got ear infections. Another sample of 159 children took xylitol and 46 of them got ear infections. The scientists believe that the proportion of ear infections in the placebo group will be greater than the xylitol group. Test this hypothesis at α = 0.025.A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percentage. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally, 65 seniors reported using drugs or alcohol within the past month, while 60 national seniors reported using them. Conduct a hypothesis test at the 5% level.NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) State the null hypothesis. H0: plocal ≠ pnational H0: plocal > pnational H0: plocal = pnational H0: plocal < pnational Part (b) State the alternative hypothesis. Ha: plocal < pnational Ha: plocal = pnational Ha: plocal ≠ pnational Ha: plocal > pnational…It was also asking for rejection region. What would that be?
- A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally, 67 seniors reported using drugs or alcohol within the past month, while 61 national seniors reported using them. Conduct a hypothesis test at the 5% level.NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) State the distribution to use for the test. (Round your answers to four decimal places.) P'local − P'national ~ ,What is your conclusion using a one sided z test if you assume α=0.01 and test the hypothesis that the proportion of colic is less among infants of mothers who don’t smoke than among the infants of mothers who smoke?What is the kurtosis for the distribution of scores with a mean of 9.02 and a mode of 3?
- A test of body reaction to the Malaysian citizens who have taken their vaccine was conducted.Selected citizens who got side effect are categorised according to their blood type and the typeof vaccine received. From a sample of 250 citizens, 150 of them were administered withSinovac while the rest received AstraZeneca. Table 4 shows the number of citizens who hadside effect after being vaccinated. i) Complete Table 4 by finding the values of M and N. ii) Does different blood type among people who had side effect relate to the type of vaccinereceived at a=0.025?You are using a z-test to test H0: u=400 vs Ha: u<400 at the a=.05 level. What would the rejection region be for this test?A cream with alpha-hydroxy acid, advertises that it can reduce wrinkles and improve the skin. In a study published in Archives of Dermatology (June 1996), 49 middle-aged women used a cream with alpha-hydroxy acid for 22 weeks. At the end of the study period, a dermatologist judged whether each woman exhibited any improvement in the condition of her skin. The results for the 49 women (where I = improved skin and N = no improvement) were: 32 I’s and 17 N’s. (a) Find a 95% confidence interval for p, the true population proportion of middle-aged women with improved skin after using this cream. Interpret the interval. (b) What assumptions are required for the confidence interval of part (a) to be statistically valid? (c) Are the assumptions for part (b) reasonably satisfied? Explain.
- Previous research has established that nationwide, for older adults, the average score on the Beck Depression Inventory (BDI-II) is 8.13 with σ = 1.56. A researcher working in a nursing home wants to know if depression levels are different for older adults living in a nursing home compared to older adults nationwide. He takes a random sample of 200 adults living in a nursing home facility and gives them each the BDI-II. The average for his sample is 8.45. Is there a difference in the BDI-II scores of those living in a nursing home compared to those living in their own homes? Test with an a = 0.01.If I have a sample of 20 people what is my T-threshold for a two-tail test and an alpha of 0.1 percent?A campaign was designed to convince car owners that they should fill their tireswith nitrogen instead of air. At a cost of about $5 per tire, nitrogen supposedlyhas the advantage of leaking at a much slower rate than air, so that the idealtire pressure can be maintained more consistently. Before spending huge sumsto advertise nitrogen, it would be wise to conduct a survey to determine thepercentage of car owners who would pay for the nitrogen. How many randomly selected car owners should be surveyed? Assume that we want to be 95% confident that the sample percentage is within three percentage points of the true percentage of all car owners who would be willing to pay for the nitrogen.