In mathematical statistics, Stat 100B, many test statistics are based on a gamma random variable that has parameter values 1 = 1/2 and α - n/2, the so called Chi-square random variable, or sums of Chi-square random variables. For statisticians, n is the number of data values they manage to get for their studies, the sample size. Suppose Y is a Chi-square random variable. What is the expected value and variance of Y? (a) n and 2n, respectively (b) 0 and 1, respectively (c) I(n/2) and Gamma(4) respectively (d) n/2 and n/4 respectively.

If random samples, each with n = 16 scores, are selected from a normal population with µ = 100 and σ = 20, how much difference, on average, should there be between a sample mean and the population mean?

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 17 16 18 15 12 14 17 17 11 (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 α = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. a: μ = 14; H1: μ < 14 b: μ = 14; H1: μ ≠ 14 c: μ > 14; H1: μ = 14 d: μ < 14; H1: μ = 14 e: μ = 14; H1: μ > 14 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume…

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:

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 143 millimeters, and a variance of 64. If a random sample of 48 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 0.2 millimeters? Round your answer to four decimal places.

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…

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…