93:7 Show that every Subop of a cyelic gp is normal
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- Look at the attached photo. There is a normality test for the two groups of INR and PCV. Interpret the data by explaining in details what each result means. Include a brief justification on why the PCR was normal and the INR was not normal.A research center claims that 25% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 700 adults in that country, 27% say that they would travel into space on a commercial flight if they could afford it. At a = 0.05, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. INU TIIUIE uIOan 0 UI auuiS I uIE UUUU y vwuuIu uavci IU apauc Un a uUITIIGI LIaI Iyntrncy couIu anuIu I. O D. At least % of adults in the country would travel into space on a commercial flight if they could afford it. Let p be the population proportion of successes, where a success is an adult in the country who would travel into space on a commercial flight if they could afford it. State H, and Ha. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to two decimal places as needed.) O A. Ho: p O B. Ha: ps OC. Ho: p> Hai p= Hai p> Ha: ps O D. Ho: pe O E. Hg:…Let X₁, X2,..., Xn be a random sample of size n from Beta (0, 1) 12 Show that the random variable - 20 Inx, has a chi-square distribution with 2n defrees of freedom
- Let {e} be a zero-mean, unit-variance white noise process. Consider a process {Y} which starts at time t = 0, and is defined recursively as follows: Let Yo = cieo, Y₁ = c₂Yo + e₁, and Y₁ = ¢₁Yt-1 + 2Yt-2 + et for t≥ 2 (as in an AR(2) process). a) Show that the process has zero mean. 1 b) For values of 01, 02 in the stationarity region for an AR (2) process, show how to choose C₁, C₂ such that both Var(Y) = Var(Y₁) and the lag 1 autocorrelation cov(Yo, Y₁) equals that of a stationary AR(2) process with parameters 01, 02. c) Once the process {Y} has been generated, show how one can transform in into a new process which has any desired mean and variance. (Remark. This gives a method for simu- lating stationary AR(2) processes.)A simple random sample of size n=200drivers were asked if they drive a car manufactured in a certain country. Of the 200 drivers surveyed, 104 responded that they did. Determine if more than half of all drivers drive a car made in this country at the α=0.05 level of significance. Complete parts (a) through (d).A random sample of 160 car crashes are selected and categorized by age. The results are listed below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the 26-45 group, 31% for the 45-65 group, and 12% for the group over 65. Calculate the chi-square test statistic χ2 to test the claim that all ages have crash rates proportional to their driving rates. Age Under 26 26 – 45 46 – 65 Over 65 Drivers 66 39 25 30
- A taxi company tests a random sample of 10 steel-belted radial tires of a certain brand and records the tread wear in kilometers, as shown below. 68,000 54,000 47,000 52,000 41,000 58,000 61,000 51,000 47,000 59,000 Note that the sample variance becomes c² times its original value if each observation in the sample is multiplied by c and unchanged if a constant is added to or subtracted from each value in the sample. Use these facts to find the standard deviation of this set of data by first dividing each observation by 1000 and then subtracting 50. For the data set that results from dividing each observation by 1000 and then subtracting 50, the variance is (Round to three decimal places as needed.) all Check answerIt has been reported that 50% of the adult population participate in computer hobbies during their leisure time. A random sample of 240 adults found that 108 engaged in computer hobbies. What is the computed z-value? conclusionA humane society claims that less than 69% of households in a certain country own a pet. In a random sample of 700 households in that country, 455 say they own a pet. At α=0.10, is there enough evidence to support the society's claim?
- Two students were independently proof-reading lecture notes. One found α typos, the other found β typos. Of those, γ typos were found by both of them. How would you estimate the total number of typos in the note?Suppose the Japanese Health Authority conducts a country wide survey to assess if men or womenhave the same likelihood of getting infected with COVID-19. A random sample of (500 + 90) and 400 women were selected, and 50% of these men and 45% of thesewomen were infected with COVID-19, respectively. What is the 91.98% condence interval for thetrue dierence in proportion of men and women who get infected with COVID-19.