10. Consider the following pairs of 6 observations: Xi Yi 5 31 11 40 4 30 5 34 3 25 2 20 β1 = 2 β0 = 20 SSE = 42 SSxy = 100 SSxx = 50 a.) Compute Sβ1. b.) Construct a 95% CI for β1.
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- 5.39 ● The following data on degree of exposure to 242Cmalpha particles (x) and the percentage of exposed cellswithout aberrations (y) appeared in the paper “Chromosome Aberrations Induced in Human Lymphocytes by D-TNeutrons” (Radiation Research [1984]: 561–573):Suppose we taken a random sample of size n from Bi(m,p). Find the CDF and PMF of X(r).suppose that the proportions of blood phenotypes in a particular population are as follows a=0.40 b=0.12 ab=0.04 o=0.44 assume the phenotype of three randomly selected individuals are independent of one another. what is the probabililty that the phenotypes of three randomly selected individuals match?
- The Weight and Blood Pressure of 26 Randomly Selected Male People in a Group ages 25 to 30 are shown in the following table. Suppose weight and blood pressure are normally and jointly distributed Y= 69.1044 + 0.4194x A)Test the hypothesis that rho = 0 and test the hypothesis that rho = 0.6The number of contaminating particles on a silicon waferprior to a certain rinsing process was determined for eachwafer in a sample of size 100, resulting in the followingfrequencies:Number of particles 0 1 2 3 4 5 6 7Frequency 1 2 3 12 11 15 18 10Number of particles 8 9 10 11 12 13 14Frequency 12 4 5 3 1 2 1a. What proportion of the sampled wafers had at leastone particle? At least five particles?b. What proportion of the sampled wafers had betweenfive and ten particles, inclusive? Strictly between fiveand ten particles?c. Draw a histogram using relative frequency on thevertical axis. How would you describe the shape of thehistogram?Suppose that a random sample of size 1 is to be taken from a finite population of size N. a. How many possible samples are there?b. Identify the relationship between the possible sample means and the possible observations of the variable under consideration.c. What is the difference between taking a random sample of size 1 from a population and selecting a member at random from the population?
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- The following data show the number of class sessions missed during a semester of SOC221 and the final grade for a sample of 8 students selected at random. Number of Sessions Missed Final Grade (x) (y) 0 96 2 88 12 68 6 91 8…assume that the data was obtained from two indepen-dent samples. That is, 28 subjects were enrolled into the study, and half were randomly assignedto the corn flakes diet, and half to the oat bran diet. After two weeks the LDL cholesterol level ofeach individual was recorded. LDL (mmol/l)Subject Corn Flakes Oat Bran1 4.61 3.842 6.42 5.573 5.40 5.854 4.54 4.805 3.98 3.686 3.82 2.967 5.01 4.418 4.34 3.729 3.80 3.4910 4.56 3.8411 5.35 5.2612 3.89 3.7313 2.25 1.8414 4.24 4.14 Questions; a) What are the appropriate null and alternative hypotheses for a two-sided test?(b) Conduct the test at the 0.05 level of significance. What is the p-value?(c) Construct a 95% confidence interval.A research center claims that that 31% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1200 adults in that country, 33% say that would travel into space on a commercial flight if they could afford it. At alpa= 0.05, isthere enough evidence to reject the research centers claim complete parts a through d below