1) Suppose tha Y is a random variable having an gamma distribution with a = 1, find the value of k such that an interval from 0 to ky is a (1 - a)100% confidence interval for the parameter ß.
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is a random variable having a Gamma distribution with .
confidence interval for parameter is .That is ,
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- A random sample of size 24 and mean 2.547 was selected from normal distribution if we want to test that the population mean is less than 5.547, knowing that the sample variance 25, the critical value for alpha =0.01 is? a. 2.807 b. 2.500 c. 2.547 d. 2.33A company is doing a hypothesis test on the variation of quality from two suppliers. Both distributions are normal, and the populations are independent. use a = 0.01 2 H0:01 HA: 01 > 2 2 02² 10₂² The standard deviation of the first sample is 2.2077 5.1485 is the standard deviation of the second sample. The test statistic is =On the first quarterly examination in Statistics and Probability of the 100 students of Grade 11 senior high school, their exam scores have a mean of 87 and a standard deviation 4. c) What percentage of students have grades between 83 and 91? Gaussian Curve
- Answer allA random sample of 10 observations from population A has sample mean of 152.3 and a sample standard deviation of 1.83. Another random sample of 8 observations from population B has a sample standard deviation of 1.94. Assuming equal variances in those two populations, a 99% confidence interval for μA − μB is (-0.19, 4.99), where μA is the mean in population A and μB is the mean in population B. (a) What is the sample mean of the observations from population B? (b) If we test H0 : μA ≤ μB against Ha : μA > μB, using α = 0.02, what is your conclusion?A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Let x, be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let x, be the empathy = 68.36. Another random sample of 31 fathers gave score of a father. A random sample of 37 mothers gave a sample mean of x, X, = 60.06. Assume that o, = 11.55 and o, = 11.45. (a) Let u, be the population mean of x, and let u, be the population mean of x,. Find a 99% confidence interval for u, - Hz. (Round your answers to two decimal places.) lower limit upper limit (b) Examine the confidence interval and explain what it means in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you about the relationship between average empathy scores for mothers compared with those for fathers at the 99% confidence level? Because the interval contains only…
- You have taken a random sample of sizen & 95of a normal population that has a population mean ofμ = 140and a population standard deviation ofo = 23. Your sample, which is Sample 1 in the following table, has a mean ofx = 141.3. (In the table, Sample 1 is indicated by "M1", Sample 2 by "M2", and so on.) (to) Based on Sample 1, plot the confidence intervals of80%and95%for the population mean. Use1,282as the critical value for the confidence interval of 80%and use1960 as the critical value for the confidence interval of95%. (If necessary, you can refer to a list of formulas .) • Write the upper limit and the lower limit on the graphs to indicate each confidence interval. Write the answers with one decimal place. • For the points (♦and ◆), write the population mean, μ = 140. 128.0 128.0 80% confidence interval 139.0 X Ś 150.0 150.0 128.0 128.0 95% confidence interval 139.0 X Ś 150.0 150.0The amount of gasoline in gallons sold by three different gas stations during one day is given by the independent random variables X1,X2, X3 each with a normal distribution. X1 has a mean µl =700 and standard deviation ơ1 55; X2 has mean u2 =700 and standard deviation o2 = 65; X3 has mean u3=900 and standard deviation 03 = 100. Suppose the prices per gallon are $2.90, $3.00 and $3.10 for X1, X2, and X3 respectively. Find the probability that the combined revenue for a given day is less than $6000. Use the z-score table. Round answer to the nearest hundredth.A random sample of 90 observations produced a mean of ?⎯⎯⎯=26.3 from a population with a normal distribution and a standard deviation ?=2.08.
