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- Suppose that the unknown Xis uniformly distributed between 0 and 2. What is the expected value ofAccording to the report about the survey performed by Company XYZ that 60% of the people think that violence has increased in the oast 4 years. In a future random sample of 250 people in a certain age of more 20 years old group, if we let X be the number of such people in that sample who think that the proposal is correct. a) What is the approximate distribution of X with parameters?The researchers decide to extend the study to a 5-year period and find that 20 of the 200 people develop a cataract over a 5-year period. Suppose the expected incidence of cataracts among 65- to 69-year-olds in the general population is 5% over a 5-year period. *7.49 Test the hypothesis that the 5-year incidence rate of cataracts is different in the excessive-sunlight-exposure group compared with the general population and report a p-value (two-sided).
- Assume that last year in a particular state with 700000 children there were 1471 children out of 32500 in a random sample who were diagnosed with Autism Spectrum Disorder. Nationally, 1 out of 88 children are diagnosed with ASD. Is there sufficient data to show that the incident rate of ASD is higher in that state than nationally? Test at the 1% level.A tax accountant would like to test the claim that the proportion of individuals who owe when filing their taxes is less than 0.20. If the z− test statistic was calculated as z=−2.11, does the tax accountant have enough evidence to reject the null hypothesis? Assume α=0.005. Move the blue dot to choose the appropriate test (left-, right, or two-tailed). Then, use the graph below to show the test statistic, p-value, and the rejection region to make a conclusion about the hypothesis test. powered by Move the blue dot to choose the appropriate test α=0.01 α=0.025 α=0.05 α=0.1 Significance level = 0.01 Select the correct answer below: There is enough evidence to suggest the proportion of individuals who owe when filing their taxes is less than 0.20. There is not enough evidence to suggest the proportion of individuals who owe when filing their taxes is less than 0.20. There is enough evidence to suggest the proportion of individuals who owe when filing their taxes is greater than 0.20.…Determine the expected value and standard deviation of a random variable Y=2X+100 when X has a pmf given by: f(x)= 0.3 if x=2 f(x)= 0.3 if x=3 f(x)= 0.1 if x=4 f(x)= 0.3 if x=5
- I need help finding the Maximum Likelihood estimator of Y1,Y2,...,Yn with a random sample size n from an exponential distribution with parameter β.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…If X is a random variable having a normal distribution with the mean μ and standard deviation σ, how do you show the moment generating function of Z=(X-μ)/σ is the moment generating function of the standard normal distribution?
