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- 1)Remove the four potential outliers of 0, 0, 8, and 20, and then obtain a new histogram without the outliers. Does the data appear to be normally distributed now? 2)Assuming that the four potential outliers of 0, 0, 8, and 20 are not recording errors, repeat the hypothesis test from part (c) (again setting up the hypothesis test and using either the critical value or p-value approach), and compare your results with that obtained in (c). Did you make a different conclusion? 3)Imagine you know have to make a recommendation/conclusion to the company that hired you: Assuming that the four potential outlies are not recording errors, and looking at the two results above, would you recommend using the first test with the outliers or the second test with the outliers removed? There is no right or wrong answer here, I am interested in what you think and your reasoning.Show that the t-distribution with r = 1 degree of freedom and the Cauchydistribution are the same.With α = .05, the two-tailed critical region for a t test using a sample of n = 20 participants would have boundaries of _____.
- Assume I observe 3 data points x1, x2, and x3 drawn independently from anunknown distribution. Given a model M, I can calculate the likelihood for each data point as Pr(x1 | M) = 0.5, Pr(x2 | M) = 0.1, and Pr(x3 | M) = 0.2. What is thelikelihood of seeing all of these data points, given the model M: Pr(x1, x2, x3 | M)?The number of visits to a website is known to have a Poisson distribution with a mean of 10 visits per minute Within what limits does Tchebysheff's Theorem suggest you would expect the number of visits to this website to lie at least 75% of the time?If the number of sample is less than 30 (n<30), what is the requirement for the population to apply the central Limit Theorem?
- Assume that out of a population of 1871 people, 30% of the population hasa particular genetic characteristic.a. Find the most likely number of the 1871 people to have thegenetic characteristic. Don’t forget to show your work.b.Let ? represent the number of people out of the 1871 whohave the genetic characteristic. Find the standard deviation for theprobability distribution of ?. Don’t forget to show your work.c. Use the range rule of thumb to find the minimum andmaximum usual value. Don’t forget to show your work. Round youranswers to the nearest whole numbersA sample of manufactured items will be selected from a large population in which 8 percent of the items are defective. Of the following, which is the least value for a sample size that will allow for the sampling distribution of the sample proportion to be assumed approximately normal?Does the data need to be normally distributed for a t-test to work?
- With α = .01, the two-tailed critical region for a t test using a sample of n = 16 subjects would have boundaries ofAn automobile manufacturer who wishes to advertise that one of its models achieves 30 mpg (miles per gallon) decides to carry out a fuel efficiency test. Six nonprofessional drivers were selected, and each one drove a car from Phoenix to Los Angeles. The resulting fuel efficiencies (in miles per gallon) are given below. 27.2 29.2 31.2 28.5 30.3 29.5 Assuming that fuel efficiency is normally distributed under these circumstances, do the data contradict the claim that true average fuel efficiency is (at least) 30 mpg? Test the appropriate hypotheses at significance level 0.05. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.) t= P-value = State the conclusion in the problem context. Reject H0. We have convincing evidence that the mean fuel efficiency under these circumstances is less than 30 miles per gallon.Do not reject H0. We have convincing evidence that the mean fuel…Are juvenile defendants who are released pending adjudication processed more slowly than those who are detained? The JDCC data set records whether a juvenile was released and the number of months it took for that juvenile’s case to reach a disposition. The sample will be narrowed to black female youth. Released juveniles (Sample 1) had a mean of 4.30 months to disposition (s = 3.86, N = 123) and detained juveniles (Sample 2) had a mean of 3.57 (s = 4.20, N = 64). Using an alpha level of .01, test the hypothesis that released juveniles’ mean time-to-adjudication is significantly greater than detained juveniles’ mean. Assume equal population variances. Use all five steps.