M 7 Two statistically independent random variables X and Y have mean values as 2 and 4 respectively. They have second moments as 8 and 25 respectively. Find the mean, second monment and variance of the random variable o = 3X - Y.
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- Total blood volume (in ml) per body weight (in kg) is important in medical research. For healthy adults, the red blood cell volume mean is about μ = 28 ml/kg.† Red blood cell volume that is too low or too high can indicate a medical problem. Suppose that Roger has had seven blood tests, and the red blood cell volumes were as follows. 34 26 40 37 28 36 29 Let x be a random variable that represents Roger's red blood cell volume. Assume that x has a normal distribution and σ = 4.75. Do the data indicate that Roger's red blood cell volume is different (either way) from μ = 28 ml/kg? Use a 0.01 level of significance. (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume that x has a normal distribution with known σ.The Student's t, since n is large with unknown σ. The standard normal, since we assume that x has a normal distribution with unknown σ.The Student's t, since we assume that x…Experiment 3: Fifteen female CSCC students and 10 male CSCC students are randomly selected to determine if the mean time studying for females is significantly more than the mean study time for males. It can be assumed that all study times are normally distributed. Are these samples independent or dependent? Find the null and alternative hypothesis. H0: Ha:Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows. 14 18 15 19 13 11 15 18 15 12 (i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) X = S = (ii) Does this information indicate that the population average HC for this patient is higher than 14? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. О Но: и 3D 14;B Hі: и 14; Hі: и %3D 14 Но: и 14 О Но: и 3D 14;B Hi: и # 14 (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 distribution and o is…
- Q3 A box contains 6 balls. Two are numbered 4, two are numbered 5, and two are numbered 6. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. If the experiment is repeated many times, find the variance (02) and standard deviation (o) of the numbers on the balls.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?A2
- Total blood volume (in ml) per body weight (in kg) is important in medical research. For healthy adults, the red blood cell volume mean is about u = 28 ml/kgt. Red blood cell volume that is too low or too high can indicate a medical problem. Suppose that Roger has had seven blood tests, and the red blood cell volumes were as follows. 31 26 43 37 32 38 29 Let x be a random variable that represents Roger's red blood cell volume. Assume that x has a normal distribution and o = 4.75. Do the data indicate that Roger's red blood cell volume is different (either way) from u = 28 ml/kg? Use a 0.01 level of significance. (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 = 28 ml/kg; H,: µ > 28 ml/kg; right-tailed O Ho: H = 28 ml/kg; H,: u < 28 ml/kg; left-tailed O Họ: H + 28 ml/kg; H,: µ = 28 ml/kg; two-tailed O Ho: H = 28 ml/kg; H,: µ + 28 ml/kg; two-tailed (b) What sampling distribution will you…Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows. 16 17 15 20 14 13 14 16 16 11 (a) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x=s= (b) Does this information indicate that the population average HC for this patient is higher than 14? Use ? = 0.01. (i) What is the level of significance? State the null and alternate hypotheses. H0: ? = 14; H1: ? < 14H0: ? > 14; H1: ? = 14 H0: ? < 14; H1: ? = 14H0: ? = 14; H1: ? > 14H0: ? = 14; H1: ? ≠ 14 (ii) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The…
