Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information. x 67 64 75 86 73 73 y 42 40 48 51 44 51 (a) Verify that Σx = 438, Σy = 276, Σx2 = 32264, Σy2 = 12806, Σxy = 20295, and r ≈ 0.823. Σx   Σy   Σx2   Σy2   Σxy   r   (b) Use a 5% level of significance to test the claim that ρ > 0. (Round your answers to two decimal places.) t   critical t   (c) Verify that Se ≈ 2.9785, a ≈ 8.997, b ≈ 0.5069, and x ≈ 73.000. Se   a   b   x

Let x be a random variable representing percentage change in neighborhood population in the past few years, and let y be a random variable representing crime rate (crimes per 1000 population). A random sample of six Denver neighborhoods gave the following information. x 31 1 11 17 7 6 y 176 37 132 127 69 53 In this setting we have Σx = 73, Σy = 594, Σx2 = 1457, Σy2 = 73,468, and Σxy = 9905.(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.) %(d) Test the claim that the population correlation coefficient ? is not zero at the 1% level of significance. (Round your test statistic to three decimal places.) t =  (e) For a neighborhood with x = 21% change in population in the past few years, predict the change in the crime rate (per 1000 residents). (Round your answer to…

Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information. x 0.326 0.302 0.340 0.248 0.367 0.269 y 2.8 7.9 4.0 8.6 3.1 11.1 (a) Verify that Σx = 1.852, Σy = 37.5, Σx2 = 0.581634, Σy2 = 293.03, Σxy = 10.915, and r ≈ -0.862. Σx   Σy   Σx2   Σy2   Σxy   r   (b) Use a 1% level of significance to test the claim that ρ ≠ 0. (Use 2 decimal places.) t   critical t ±     (c) Verify that Se ≈ 1.9379, a ≈ 26.656, and b ≈ -66.110. Se   a   b

Let a be a random variable representing the percentage of protein content for early bloom alfalfa hay. The average percentage protein content of such early bloom alfalfa should be u = 17.2%. A farmer's co-op is thinking of buying a large amount of baled hay but suspects that the hay is from a later summer cutting with lower protein content. A small amount of hay was removed from each bale of a random sample of 50 bales. The average protein content from the samples was determined by a local agricultural college to be -15.8% with a sample standard deviation of S = 5.3%- At a = .05, does this hay have lower average protein content than the early bloom alfalfa?

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.  x 67 70 69 81 65 86 y 51 54 45 56 50 49 Given that ∑x = 438, ∑y = 305, ∑x2 = 32,332, ∑y2 = 15,579, ∑xy = 22,302, and r = 0.226, find the P-value for a test claiming that ρ is greater than zero.   0.25 >  P-value  > 0.10   0.10 >  P-value  > 0.05   0.40 >  P-value  > 0.25   P-value  < 0.0005   P-value  > 0.40X

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information. 73 73 X 67 64 75 86 y 42 39 48 51 44 51 (a) Find Ex, Ey, Ex2, Ey2, Exy, and r. (Round r to three decimal places.) Ex=438✔✔ 2y = 275| v Ex2 32264✔✔ Ex² = Ey212727 Exy = 20231| r = .645 X

Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information. x 0.318 0.272 0.340 0.248 0.367 0.269 y 3.4 8.0 4.0 8.6 3.1 11.1  Σx = 1.814, Σy = 38.2, Σx2 = 0.559262, Σy2 = 298.34, Σxy = 10.8736, and r ≈ -0.874.     (e) Find a 95% confidence interval for y when x = 0.35. (Use 2 decimal places.) lower limit % upper limit      (g) Find a 95% confidence interval for β and interpret its meaning. (Use 2 decimal places.) lower limit   upper limit

Suppose that the contagious period of COVID-20 has an average of 7 days, and follows a chi-square distribution.  Let X measure the contagious period for a randomly selected specimen of the COVID-20 virus. State the distribution of the random variable X. Group of answer choices X∼χ2(6) X∼Student′st(7) X∼χ2(7) X∼Continuous(7)     A friend of yours has COVID-20 and the doctors have told her that she has had it for 10 days.  Compute the probability that they are still contagious.  (I.E. compute the probability that X is greater than or equal to 10 days.)

Let x be a random variable that represents blood glucose level after a 12-hour fast. Let y be a random variable representing blood glucose level 1 hour after drinking sugar water (after the 12-hour fast). Units are in milligrams per 10 milliliters (mg/10 ml). A random sample of eight adults gave the following information. Σχ - 64.2; Σ ? = 528.24; Ey = 90.4; Ey² = 1063.88; Exy = 741.77 6.2 8.6 7.0 7.5 8.3 6.9 10.0 9.7 y 9.7 10.3 10.9 11.5 14.2 7.0 14.6 12.2 Find the equation of the least-squares line. (Round your answers to three decimal places.) Find the sample correlation coefficient r and the sample coefficient of determination r. (Round your answers to three decimal places.) r = 2 = If x = 7.0, use the least-squares line to predict y. (Round your answer to two decimal places.) y = Find an 80% confidence interval for your prediction. (Round your answers to two decimal places.) lower limit mg/10 ml upper limit mg/10 ml Use level of significance 1% and test the claim that the…

Let x be a random variable representing percentage change in neighborhood population in the past few years, and let y be a random variable representing crime rate (crimes per 1000 population). A random sample of six Denver neighborhoods gave the following information. x 31 1 11 17 7 6 y 176 37 132 127 69 53 In this setting we have Σx = 73, Σy = 594, Σx2 = 1457, Σy2 = 73,468, and Σxy = 9905. (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 four decimal places.) x =  y =  b =  ŷ =  +  x