A psychology professor claims that the variance of IQ scores for college students is σ^2 = 100. Let X1, X2,…, X23 be a random sample of n = 23 IQ scores and assume these scores come from a N(µ, σ^2) distribution. Let S^2 = (1/22) ∑_(i=1 to 23) (Xi – X bar)^2 be the sample variance of these scores. The observed value of S^2 = 147.82. Show that the Var(S^2) = 10000/11. Thus, the standard deviation of S^2 is 30.15.
properties of chi square distribution is used. For further query in above, comment.
A psychology professor claims that the variance of IQ scores for college students is σ^2 =...
Let X1, . . . , Xn be a random sample from a normal distribution, Xi ∼ N(µ, σ^2 ). Find the UMVUE of σ ^2 .
Let X1,X2, , Xn be a random sample from a normal distribution with a known mean μ (xi-A)2 and variance σ unknown. Let ơ-- Show that a (1-α) 100% confidence interval for σ2 is (nơ2/X2/2,n, nơ2A-a/2,n). Let X1,X2, , Xn be a random sample from a normal distribution with a known mean μ (xi-A)2 and variance σ unknown. Let ơ-- Show that a (1-α) 100% confidence interval for σ2 is (nơ2/X2/2,n, nơ2A-a/2,n).
A college professor claims that the entering class this year appears to be smarter than entering classes from previous years. He tests a random sample of 22 this year's entering students and finds that their mean IQ score is 119, with standard deviation of 15. The college records indicate that the mean IQ score for entering students from previous years is 112. If we assume that the IQ scores of this year's entering class are normally distributed, is there enough...
A college professor claims that the entering class this year appears to be smarter than entering classes from previous years. He tests a random sample of 16 of this year's entering students and finds that their mean IQ score is 116, with standard deviation of 10. The college records indicate that the mean IQ score for entering students from previous years is 113. If we assume that the 10 scores of this year's entering dass are normally distributed, is there...
Independent random samples X1, X2, . . . , Xn are from exponential distribution with pdfs , xi > 0, where λ is fixed but unknown. Let . Here we have a relative large sample size n = 100. (ii) Notice that the population mean here is µ = E(X1) = 1/λ , population variance σ^2 = Var(X1) = 1/λ^2 is unknown. Assume the sample standard deviation s = 10, sample average = 5, construct a 95% large-sample approximate confidence...
Problem 2. Problem 1 doesn't need to be done, it's here for reference 166 Branching processes is a branching process whose .... is a branchin the result zes have mean μ (s l ) and variance σ 2, then var( ZnJun of Problem 9.6.1 to show that, if Zo. z 2. Use ditioning on the value of Zm, show th ose fa outition theorem and conditioning on the value of Z 9.6 Problems I. Let X1 , X2. . ....
2. Biased and unbiased estimation for variance of Bernoulli variables A Bookmark this page 2 points possible (graded) Let X1, X, bed. Bernoull random variables, with unknown parameter PE (0,1). The aim of this exercise is to estimate the common variance of the X First, recall what Var (X) is for Bernoulli random variables. Var (X) - Let X, be the sample average of the Xi. X. - 3x Interested in finding an estimator for Var(X), and propose to use...
QUESTION 2 Let Xi.. Xn be a random sample from a N (μ, σ 2) distribution, and let S2 and Š-n--S2 be two estimators of σ2. Given: E (S2) σ 2 and V (S2) - ya-X)2 n-l -σ (a) Determine: E S2): (l) V (S2); and (il) MSE (S) (b) Which of s2 and S2 has a larger mean square error? (c) Suppose thatnis an estimator of e based on a random sample of size n. Another equivalent definition of...
Professor Jennings claims that only 35 of the students at Hora College work while attending school. Deon Renata thinks that the professor has underestimated the number of students with part-time or sample of 78 students shows that 37 have jobs. Do the data indicate that more than 35% of the students have Jobs use a level of significance time jobs. A random What are we testing in this pr Single proportion (a) What is the level of significance? State the...
MAT 107 Project: Age of Students in College Professor Sumner Collect Data: (5 points) You will need to ask 30 college students their age. The students can attend any college or university. Use the table below to input the data you collected. If you do the work for this project by hand, you must show the work you do to arrive at your results to earn full credit. If you use technology (computer, calculator, etc.) to obtain the results, you...