6. If $X_{1}, X_{2}, X_{3}$, and $X_{4}$ are (pairwise) uncorrelated random variables, each having mean 0 and variance 1 , compute the correlations of (a) $X_{1}+X_{2}$ and $-X_{2}+X_{3}$. (b) $X_{1}+X_{2}+X_{3}$ and $X_{3}+X_{4}$. CS. JG.083
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- AP Stats Free Res ponse - Period 6 Name Date Many people consider Fosco University every year for its large graduate programs (estimated over 7,500 students each year). Fos co University provides housing for 10% of the gradua te students on campus. The housing office thinks that the percentage of graduate students looking for campus housing may be more than 10%. The office decides to survey a random sa mple of graduate students, and 62 of the 481 respondents say that they are looking for housing on campus. (a) With the results of the survey, would you recommend that the Fosco U niversity consider increasing the amount of housing on campus for graduate students? Give the appropriate evidence/test to support your dlaim. Use a significance level of.05. (b) In addition to the 481 graduate students who completed the survey, an additional 19 students did not respond. If the 19 responded, would you change your recommendation? Explain and show work.During the exam you will be using a sample of 500 adults with the following variables: ● genhelf - variable recording general self-reported health coded 1 = very good, 2 = good, 3 = fair, 4 = poor ● sbp - variable recording systolic blood pressure age - age of the respondent in years • sex-coded 1 = male and 2 = female ● hi_sbp - indicator of high blood pressure coded 1 if the respondent's sbp is 130 or higher and 0 otherwise What type of variable is genhelf? O Discrete Continuous Nominal O OrdinalDr. Watts is a pediatrician. His group did some research on the sleep habits of children less than 24 months old. They found a weak negative correlation between a child’s age and the number of hours per day he or she slept. What does this mean? As a child’s age increases, the hours of sleep decreases in a nearly perfect pattern. As a child’s age increases, the hours of sleep increases in a nearly perfect pattern. As a child’s age increases, the hours of sleep decreases but the relationship is not perfect. As a child’s age increases, the hours of sleep increases but the relationship is not perfect.
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- If I was calculating the variance of this list of numbers (attached), do I need to include the "no home games" as a 0 and base the calculation on 14 entries? Or do I just leave them out completely and base the calculation on 12 entries?The service times for customers coming through a checkout counter in a retail store are independentrandom variables with mean 1.5 minutes and the variance 1.0. Approximate the probability that 100customers can be served in less than (a) 2 hours (b) 3 hours of total service time.An "extraneous variable" is not a problem unless it with the independent variable O is identical systematically co-varies is not correlated Wait! An "extraneous variable" is by definition never a problem, that's what "extraneous" means.
- Of a random sample of 100 college students, 35 expected to achieve a higher standard of living than their parents, 43 expected a lower standard of living, and 22 expected about the same standard of living as their parents. Do these data present strong evidence that, for the population of students, more expect a lower standard of living compared with their parents than expect a higher standard of living?A candy maker offers Child and Adult bags of jelly beans with different color mixes. The company claims that the Child mix has 30% red jelly beans, while the Adult mix contains 15% red jelly beans. Assume that the candy maker’s claim is true. Suppose we take a random sample of 50 jelly beans from the Child mixand a separate random sample of 100 jelly beans from the Adult mix. Let ?^ and ?^ be the sample ??proportions of red jelly beans from the Child and Adult mixes, respectively.a. What is the shape of the sampling distribution of ?^ − ?^ ? Why???b. Find the mean of the sampling distribution. Show your work.c. Find the standard deviation of the sampling distribution. Show your work.The proportion of drivers who use seat belts depends on things like age (young people are more likely to go unbelted) and gender (women are more likely to use belts). It also depends on local law. In New York City, police can stop a driver who is not belted. In Boston at the time of the study, police could cite a driver for not wearing a seat belt only if the driver had been stopped for some other violation. Here are data from observing random samples of female Hispanic drivers in these two cities. (a) Verify that the 95% CI for the difference in the proportions of female Hispanic drivers in the two cities who wear seat belts pNY −pBT is (0.149,0.353). Show your computation.(b) Determine if the following statements are true or false, and explain your reasoning if you identify the statement as false. i. There was strong evidence that pNY > pBT.ii. 95% of random samples of 220 female Hispanic drivers in New York City and 117 female Hispanic drivers in Boston will yield differences…