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- It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico: x 5.00 5.25 5.75 6.75 7.00 y 8 15 13 49 71 Find the equation of the least squares line . Round a and b to three decimal places. Find the correlation coefficient r for the elevation and percentage of unidentified artifacts (no specific cultural affiliation) at a given elevationLet x represent the hemoglobin count (HC) in grams per 100 milliliters of whole blood. The distribution for HC is approximately normal with μ = 14 for healthy adult women. Suppose that a female patient has taken 12 laboratory blood samples in the last year. The HC data sent to her doctor is listed below. We would like to know if the data indicates this patient has significantly high HC compared to the population. 14,19,16,14,19,19,14,21,17,17,14,17 Give the p-value and interpret the results. a) p = 0.0012; Based on 5% significance level, I will reject the null hypothesis and conclude this patient has a high HC level. b) p = 0.0012; Based on 5% significance level, I will fail to reject the null hypothesis and conclude this patient does not have a high HC level. c) p = 0.0023; Based on 5% significance level, I will reject the null hypothesis and conclude this patient has a high HC level. d) p = .1053; Based on 5% significance level, I will fail to reject the null hypothesis and…1 (a) Discuss the two expressions -x;- )² and E(x;- )², both of which are used (n-1) i=1 to measure the spread of a set of observations x1, x2, . .., X. (b) A random sample of n observations is taken from a distribution; the sum of the observations is t, and the sum of the squares of the observations is 12. Explain how to estimate the mean and the variance of the distribution from which the random sample was taken. (c) Given the random sample described in part (b), write down expressions (based on 11 and t2) for estimates of the mean and variance of the mean of a further, independent, random sample of size m , from the original distribution. (d) Given that n = 25, 1, = 400 and t2 = 8800, construct a 99% confidence interval for the mean of the distribution, and use it to test whether or not this mean could be 20.
- It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico: x 5.75 6.25 6.75 7.75 8.25 y 31 26 38 74 72 Find the value of the coefficient of determination r2. Group of answer choicesLet x represent the hemoglobin count (HC) in grams per 100 milliliters of whole blood. The distribution for HC is approximately normal with μ = 14 for healthy adult women. Suppose that a female patient has taken 12 laboratory blood samples in the last year. The HC data sent to her doctor is listed below. We would like to know if the data indicates this patient has significantly high HC compared to the population. 22,17,20,17,17,14,16,21,15,21,15,22 Give the p-value and interpret the results. a) p = .1053; Based on 5% significance level, I will fail to reject the null hypothesis and conclude this patient does not have a high HC level. b) p = .0562; Based on 5% significance level, I will fail to reject the null hypothesis and conclude this patient does not have a high HC level. c) p = 0.0003; Based on 5% significance level, I will fail to reject the null hypothesis and conclude this patient does not have a high HC level. d) p = 0.0003; Based on 5% significance level, I will reject the…Green Auto periodically has a special week-long sale. As part of the advertising campaign, Green runs one or more television commercials during the weekend preceding the sale. Given are seven observations for two variables, x and y. Number of TV Ads (x) 1 3 2 1 3 4 3 Number of Cars Sold (y) 14 24 15 13 27 28 21 (E). Compute the coefficient of determination R^2. Comment on the goodness of fit. (F). Use the F test to test the hypotheses (α = 0.05): ??0: ??1=0; ????: ??1≠0 State the conclusion and the reasons (i.e., rejection rule).
- Let X-T(4) and Y~ x2 (4). The following plot depicts the cumulative distribution functions of X and Y. We don't know which is which. The horizontal lines have values 25% and 75%. We denote by q1 the x-coordinate correponding to the red point and by q2 the x-coordinate corresponding to the blue point. Which of the following statements are true? 1.00 - 0.75 0.50 - 0.25+ 0.00 - The answer is : The cdf of X corresponds to the red curve while the one of Y corresponds to the blue curve. Can you explain why? DensityThe following table contains data on the joint distribution of age (Age) and average hourly earnings (AHE) for 25 to 34 year-old full-time workers with an educational level that exceeds a high school diploma in 2012. Download the data from the table by clicking the download table icon. A detailed description of the variables used in the dataset is available here. Use a statistical package of your choice to answer the following questions. Compute the marginal distribution of Age. Marginal distribution of Age = 25 .0754 26 .0797 27 .0947 Age (years) 28 30 29 .0953 0983 .1105 31 .1109 (Round your response to four decimal places) Compute the mean of AHE for Age = 33; that is, compute, E(AHE |Age = 33). E(AHE |Age=33) = (Round your response to four decimal places) 32 .1134 33 1134 34 1085Write an absolute value function f(t) to describe an individual variance from normal body temperature where t is the individual current temperature
- An individual’s income varies with his or her age. The following table shows the median income I of males of different age groups within the United States for 2012. For each age group, let the class midpoint represent theindependent variable, x. For the class “65 years and older,” we will assume that the class midpoint is 69.5. (a) Use a graphing utility to draw a scatter diagram of thedata. Comment on the type of relation that may existbetween the two variables.(b) Use a graphing utility to find the quadratic function ofbest fit that models the relation between age and medianincome.(c) Use the function found in part (b) to determine the age atwhich an individual can expect to earn the most income.(d) Use the function found in part (b) to predict the peakincome earned.(e) With a graphing utility, graph the quadratic function ofbest fit on the scatter diagram.A chi square test tells us: a. Whether two continuous variables are correlated with each other. b. Whether two discrete variables are independent of each other c. The amount of variation in one variable explained by the other d. Which categories of one variable are associated with which categories of the other variable