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 (a) Verify that Σx = 1.814, Σy = 38.2, Σx2 = 0.559262, Σy2 = 298.34, Σxy = 10.8736, and r ≈ -0.874. 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 ≈ 1.8023, a ≈ 25.226, and b ≈ -62.380. Se   a   b

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 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 0.336 0.296 0.340 0.248 0.367 0.269 y 3.2 7.5 4.0 8.6 3.1 11.1 (b) Use a 10% level of significance to test the claim that ρ ≠ 0. (Use 2 decimal places.) t   critical t ±   (d) Find the predicted percentage of strikeouts for a player with an x = 0.288 batting average. (Use 2 decimal places.) %(e) Find a 95% confidence interval for y when x = 0.288. (Use 2 decimal places.) lower limit  % upper limit  % (f) Use a 10% level of significance to test the claim that β ≠ 0. (Use 2 decimal places.) t   critical t ±   (g) Find a 95% confidence interval for β and interpret its meaning. (Use 2 decimal places.) lower limit   upper limit   please show steps and work

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

I need help with parts D and C only.  Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 2.9%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7   4.8   6.0   4.9   4.0   3.4   6.5   7.1   5.3   6.1 The sample mean is = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 4.1%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.1%? Use α = 0.01. (a) What is the level of significance? (Enter a number.)State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: μ = 4.1%; H1: μ > 4.1%; right-tailedH0: μ = 4.1%; H1: μ < 4.1%; left-tailed     H0: μ > 4.1%; H1: μ = 4.1%; right-tailedH0: μ = 4.1%; H1: μ ≠ 4.1%; two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since n is large with…

Given that z is a standard normal random variable, find the z value for the following situations: a. The area to the left of z is .2119 b. The area to the right of z is .6915 c. The area between 0 and z is .4332

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

Let Y = 3X – 1, where X is a random variable that is distributed uniformly from 10 to 50. Answer the following questions.a. What is the probability that X takes any value from 20 to 30? Draw the distribution and identify this probability in the distribution. Show your calculations.b. Calculate the expected value of X in addition to the variance and standard deviation of X. Show your calculations.c. Calculate the expected value of Y in addition to the variance and standard deviation of Y. Show your calculations.

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 73 84 88 63 76 85 y 46 45 55 41 51 53 Given that 3.755, a*13.677, b*0.445, x 78.167, Ex=469, y = 291, Ex² = 37,099, and y² = 14,257, find a 90% confidence interval for y when x=79. tc = 2.132 O between 40.9 and 56.9 O between 40.2 and 57.5 O between 40.1 and 57.6 O between 39.9 and 57.8 O between 40.4 and 57.4