Let X bar, Y bar, S2X, and S2Y be the respective sample means and unbiased estimates of the variances obtained from independent samples of sizes n and m from the normal distributions N( Icirc frac14 X, Iuml 2X) and N( Icirc frac14 Y, Iuml 2Y), where Icirc frac14 X, Icirc frac14 Y, Iuml 2X, and Iuml 2Y are unknown If Iuml 2X Iuml 2Y d, a known constant, (c) Argue that the two random variables in (a) and (b) are independent (d) With these results, construct a random variable (not depending upon Iuml 2Y) that has a t distribution and that can be used to construct a confidence interval for Icirc frac14 X Icirc frac14 Y Y) (x HY) is N0 1 (a) Argue that b) Argue that mix, (m (n 1)S2 isr'(n m 2) X m 2)

Question: Let X-bar, Y-bar, S2X, and S2Y be the respective sample means and unbiased estimates of the variances obtained from independent samples of sizes n and

Let X-bar, Y-bar, S2X, and S2Y be the respective sample means and unbiased estimates of the variances obtained from independent samples of sizes n and m from the normal distributions N(Î¼X, Ïƒ2X) and N(Î¼Y, Ïƒ2Y), where Î¼X, Î¼Y, Ïƒ2X, and Ïƒ2Y are unknown. If Ïƒ2X/Ïƒ2Y = d, a known constant,

(c) Argue that the two random variables in (a) and (b) are independent.
(d) With these results, construct a random variable (not depending upon Ïƒ2Y) that has a t distribution and that can be used to construct a confidence interval for Î¼X ˆ’ Î¼Y.

-Y) (x HY) is N0.1 (a) Argue that b) Argue that mix, (m- (n 1)S2 isr'(n+m-2). X +-m-2)

Step by Step Solution

★★★★★

3.45 Rating (174 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

From a b and c we know d Has a tn m 2 ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

579-M-S-P-E (736).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let S2X and S2Y be the respective variances of two independent random samples of sizes n and m from N(Î¼X, Ï2X) and N(Î¼Y, Ï2Y). Use the fact that F =...

Let X and Y equal the hardness of the hot and cold water, respectively, in a campus building. Hardness is measured in terms of the calcium ion concentration (in ppm). The following data were...

Let X and Y denote the tarsus lengths of male and female grackles, respectively. Assume that X is N(X, 2x) and Y is N(Y, 2Y). Given that n = 25, x = 33.80, s2 x = 4.88, m = 29, y = 31.66, and s2y =...

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

The best definition for nonparametric statistics I can think of is when data does not fit inside the normal parameters of a normal distribution, it calls for the use of this statistical method....

Possible Multiple Choice Questions for the Exam. Focus on the topics discussed in class. Chapter 1 Multiple Choice Identify the choice that best completes the statement or answers the question. ____...

2. 3. 4. 5. 6. 7. The Bem Sex Role Inventory (BSRI) provides independent assessments of masculinity and femininity in terms of the respondent's self-reported possession of socially desirable,...

1. Calculate the sample size needed given these factors: one-tailed t-test with two independent groups of equal size small effect size (see Piasta, S.B., & Justice, L.M., 2010) alpha =.05 beta = .2...

Answer the following True/False, Multiple Choice, Fill in blank as QUICKLY AS POSSIBLE*. Please let them be correct answers. No explanation needed. 1 When conducting a one-sample t test, if a sample...

Heather Smith is considering a bond investment in Locklear Airlines. The $1,000 par value bonds have a quoted annual interest rate of 11 percent and the interest is paid semiannually. The yield to...

Glide Shoe Company is planning a one-month campaign for May to promote sales of one of its two shoe products. A total of $125,000 has been budgeted for advertising, contests, redeemable coupons, and...

If investors expect a total return of 1 3 . 4 0 % , what will be Goodwin s expected dividend and capital gains yield in two years that is , the year before the firm begins paying dividends? Again,...

Describe and assess the problem identification of Walkers and AMV BBDO, and the solution they proposed in terms of objectives, target groups and creative ideas.

Calculate the marginal probabilities from the following table of jointprobabilities. 231 3 AR

Refer to Exercise. a. Determine P(A1B1). b. Determine P(A2B1). c. Did your answers to parts (a) and (b) sum to 1? Is this a coincidence? Explain.

Refer to Exercise 6.17. Calculate the following probabilities. a. P(A1B2) b. P(B2A1) c. Did you expect the answers to parts (a) and (b) to be reciprocals? In other words, did you expect that P(A1B2)...

#12 Question # 12 You wish to estimate the proportion of all voters in California who plan to vote in favor of a certain ballot measure. Obtain a sample size that will ensure a margin of error of at...

Mr. V is interested in testing if students evaluations differ from his class before and after they went online. He randomly asks 7 students to rate how much they enjoyed the class on a level of 1 to...

Discuss in a two page, APA formatted paper, how analytics and modeling are being used in an advanced state in an organization you're familiar with. Remember, the two pages is your own written work...