The marginal distributions of two random variables X and Y, together with some values of their joint distribution, are given in the table below. Fill in the table in such a way that X and Y are independent random variables. Value of Y -2 Value of X .32 .80 3 .08 .20 .40 .40 .20 1.00
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- Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with ? = 3.2%. 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 x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is ? = 4.3%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.3%? Use ? = 0.01. (a) What is the level of significance?State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: ? > 4.3%; H1: ? = 4.3%; right-tailedH0: ? = 4.3%; H1: ? ≠ 4.3%; two-tailed H0: ? = 4.3%; H1: ? < 4.3%; left-tailedH0: ? = 4.3%; H1: ? > 4.3%; right-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 unknown ?.The standard normal, since we assume that x has a normal…Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml). 91 88 82 103 97 108 84 91 The sample mean is x ≈ 93.0. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that ? = 12.5. The mean glucose level for horses should be ? = 85 mg/100 ml.† Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use ? = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: ? = 85; H1: ? > 85; right-tailed H0: ? > 85; H1: ? = 85; right-tailed H0: ? = 85; H1: ? ≠ 85; two-tailed H0: ? = 85; H1: ? < 85; left-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.…Evaluation 1. Samples of size n were randomly selected from the population with means and variances given below. In each case, find the mean, variance, and the variance of the sampling distribution of the means. a. n = 49; μ = 25; o² = 6.25 b. n = 55; μ = 10; o² = 9 2. A random sample of n = 100 measurements is obtained from a population with μ = 55 and o = 20. Describe the sampling distribution of means by computing the (a) mean of the sampling distribution of means μ, (b) variance of the sampling distribution of means o, and the (c) standard deviation of the sampling distribution of means o.
- Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml). 94 87 83 104 98 108 84 89 The sample mean is x = 93.4. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that o = 12.5. The mean glucose level for horses should be u = 85 mg/100 ml.t Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Ho: H = 85; H,: u + 85; two-tailed O Ho: H = 85; H: µ > 85; right-tailed O Ho: H > 85; H,: µ = 85; right-tailed O Ho: H = 85; H,: µ < 85; left-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since we assume…Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml). 95 88 80 107 101 108 84 87 The sample mean is x ≈ 93.8. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that ? = 12.5. The mean glucose level for horses should be ? = 85 mg/100 ml.† Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use ? = 0.05. (a) Compute the z value of the sample statistic. (Round your answer to two decimal places.) (b) Find (or estimate) the P-value. (Round your answer to four decimal places.)Briefly explain how increasing sample size influences each of the following. Assume that all other factors are held constant. Does tach increase, decrease, or stay the same? (M-u) (M-u)Vn The size of the Z-score Z. = M-u – OM (M-u) The size of Cohen's d d = (Mcr-u) (Mcr-u)vn The power P( 2Z> Mcritical-µu
- A through F trying to double check my answersLet x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with ? = 2.5%. 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 ? = 4.9%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.9%? Use ? = 0.01. (c) Find (or estimate) the P-value. (Enter a number. Round your answer to four decimal places.) ?Sketch the sampling distribution and show the area corresponding to the P-value. (Select the correct graph.)Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with o = 2.4%. 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 x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is u = 4.8%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.8%? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? Ho: H = 4.8%; H1: µ ± 4.8%; two-tailed Ho: H = 4.8%; H1: µ > 4.8%; right-tailed Ho: H = 4.8%; H1: µ 4.8%; H1: µ = 4.8%; right-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 unknown o. The Student's t, since we assume that x has a normal distribution with known o. The standard normal, since…
- Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with ? = 1.8%. 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 6.1Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml). 95 86 80 103 99 110 82 87 The sample mean is x = 92.8. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that o = 12.5. The mean glucose level for horses should be u = 85 mg/100 ml.t Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Ho: H = 85; H,: µ + 85; two-tailed O Ho: H = 85; H,: µ > 85; right-tailed O Ho: H = 85; H,: u 85; H,: u = 85; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since we assume that x has a normal…The joint distribution of two random variables X and Y is tabulated below. Complete the table by completing the marginal distributions of X and Y of.
