need help with whole page, first part might be wrong 6. In a given population of

Question

need help with whole page, first part might be wrong

6. In a given population of people, male earnings have a mean of $45,000 and a standard eviation of $12,000. Female earnings have a mean of $40,000 and a standard deviation of S18,000. We randomly select a one male and one female. What is the expected value and dard deviation of the difference in their earnings (Difference-Male-Female) A. E(Difference)- E(Male - Female)- B. V(Difference)- C. Standard Deviation(Difference)- 1 oks ce) - Eptale -Female) Clave-Cost) 345000- 7. We repeat the above experiment 25 times. On each repetition, we record the random variable D, the difference in earnings. Then we average the 25 differences to form the sample average of the difference. What is the expected value and standard error of the sample average? A. E(D25) B. Standard Error (D25) 8. Instead of selecting males and emales separately, we select a couple (one male and one female). The earnings of members of couples have a strong and positive correlation of 0.8. Let C denote the combined earnings (male + female) for a randomly selected couple. What is the mean, variance and standard deviation of the random variable C? A. E(C) E(Male + Female)- B. V(C) V(Male + Female)- C. Standard Deviation(C) We select 49 couples, calculate the combined earnings of each couple, and then calculate the sample average of the combined earnings. What is the expected value and standard error of the sample average? A. EC,9)- 9. B. Standard Error (C49)-

Explanation / Answer

(6)

In this part you have correctly calculated the E(difference) part but the V(Difference) is not correct. It's calculated as shown below:

Vdifference = Vmale + Vfemale = (12000)2 + (18000)2 = 468000000

Next,

Standard deviation(Difference) = (Vdifference)0.5 = (468000000)0.5 = 21633.31

(7)

By the central limit theorem, we have:

E(D25) = E(Difference)

This is the result because of the CLT theorem.

So, we have:

E(D25) = $5000

Next, when we have a distirbution of sample averages, we have the following formula for calculating the standard error of the distribution:

Standard error = (Vmale/n + Vfemale/n)0.5

Here, n denotes the sample size.

So, n = 25

Thus we have:

Standard error = ((12000)2/25 + (18000)2/25)0.5 = 4326.66

Only 1 question is allowed per chegg question I haver answered two for you. Please ask others in a separate question.

Hope this helps !

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.