Example 19: (H.W) Let Y,Y, be an order statistic of a sample space with size 2. Let Y, = X,, Y, = X,. Find g(y,.y2) and g(y,). Example 20: (H.W) Let Y,.Y,,Y, be an order statistic of a sample space with size 3 having the p.d.f. S(x) =1 I
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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- Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 150 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. a) State the appropriate null and alternate hypotheses. b) Find the P-value. c) Should a change be made?Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 149 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. P-value?A sociologist is interested in the relation between x = number of job changes and y = annual salary (in thousands of dollars) for people living in the Nashville area. A random sample of 10 people employed in Nashville provided the following information. x (number of job changes) 5 3 6 6 1 5 9 10 10 3 y (Salary in $1000) 36 37 34 32 32 38 43 37 40 33 Σx = 58; Σy = 362; Σx2 = 422; Σy2 = 13,220; Σxy = 2,165 (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.) x = y = b = ŷ = + x (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. (c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.) r = r2 = What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)%
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- An agricultural scientist tests six types of fertilizer, labeled A, B, C, D, E, and F, to determine whether any of them produces an increase in the yield of lima beans over that obtained with the current fertilizer. For fertilizer C, the increase in yield is statistically significant at the 0.05 level. For the other five, the increase is not statistically significant. The scientist concludes that the yield obtained with fertilizer C is greater than that of the current fertilizer. Explain why this conclusion is not justified.Let X1, …, Xn be a random sample from a N(μ, σ²) population. Find the MLEs of μ and of σ.4. Compute F-statistics and infer genetic differentiation. Flower color of desert snow (Linanthus parryae) is controlled by one locus with two alleles (P and W, for pink and white, respectively). A river divides the area into two regions. Three subpopulations (Demes) were sampled from each region, with genotype frequencies shown by Region and Deme in the table below.
- Suppose a simple random sample of size n equals 1000 is obtained from a population whose size is N equals 2 comma 000 comma 000 and whose population proportion with a specified characteristic is p equals 0.75. Complete parts (a) through (c) below.From time to time, the UTM Human Resource (UTMHR) department observes various employees fortheir work productivity. Recently UTMHR wanted to check whether the four employees at theDepartment XYZ counters, serve on average the same number of customers per hour. The HR managerobserved each of the four employees for a certain number of hours. The following Table 5 gives thenumber of customers served by the four employees during each of the observed hours. employee a employee b employee c employee d 19 14 11 24 21 16 14 19 26 14 21 21 24 13 13 26 18 17 16 20 employee a employee b employee c employee d mean 21.6 14.8 15.0 22.0 s 3.4 ? 3.8 ? c) Find variance between sample,d) Find variance within sample, e) Calculate the test statistic, F.f) Determine the numerator and denominator.g) Find the critical value of F at the 5% significance level, and test the claim that the mean numberof customers served per hour by each of these four employees is…From time to time, the UTM Human Resource (UTMHR) department observes various employees fortheir work productivity. Recently UTMHR wanted to check whether the four employees at theDepartment XYZ counters, serve on average the same number of customers per hour. The HR managerobserved each of the four employees for a certain number of hours. The following Table 5 gives thenumber of customers served by the four employees during each of the observed hours. employee a employee b employee c employee d 19 14 11 24 21 16 14 19 26 14 21 21 24 13 13 26 18 17 16 20 a) Define the hypothesis null, H0 and hypothesis alternative, H1.b) Given below are means and standard deviation for some of the employees. Calculate thestandard deviation for Employee B and D.