12 Sampling Distributions Part 1 (1)

# You have a sample of customers who purchased family

This preview shows pages 34–40. Sign up to view the full content.

market. You have a sample of customers who purchased family sedans in 2003. Assume that purchase price has a normal distribution with a mean of \$25,000 and a standard deviation of \$5,000. You draw a random sample of n=25 customers. 34

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
1. What is the probability that the sample mean is between \$24K and \$26K? 3. What is the probability that one customer’s purchase is between \$24K and\$26K? x ~ N(25,000, 5,000/√25) = N(25,000,1,000) ̅ P(2 4 ,0 0 0 < x < 26,000) = 1 ̅ 2*P(x < ̅ 24,000) = 1 – 2 *NORM.DIS T(2 4 0 0 0 , 2 5 0 0 0 , 1 0 0 0 , TRUE) = 0 .6 8 2 7 x ~ N(25000, 5000) P(2 4 ,0 0 0 < x < 26,000) = 1 2*P(x < 24,000) = 1 – 2 *NORM.DIS T(2 4 0 0 0 , 2 5 0 0 0 , 5 0 0 0 , TRUE) = 0 .1 5 8 5 = 1 – 2 *NORM.S .DIS T(-1 ,TRUE) = .6 8 2 7 Example: Family Sedan Purchase Price 35
Example: Homeowner’s insurance Liberty Mutual decided to use data to calculate the parameters of interest for insurance cost and sampling distribution of the insurance cost for accounting purposes. In addition to this, they are interested in the proportion of insurance costs that are greater than a certain number for risk estimation. Because of the time and budget limitations they can not analyze the whole data. Therefore, they will use a small sample from the population. Assume that the mean cost of homeowner’s insurance is \$754 and the standard deviation is σ = \$227. Suppose you draw a simple random sample of n=100 insurance policies. 36

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
1. What is the sampling distribution of the mean cost of homeowner’s insurance? 2. What is the probability that the random sample of HO insurance policies will have a sample mean of more than \$20 greater than the population mean? 3. If we increase n to 400, what is the sampling distribution of the mean cost of homeowner’s policies? 4. What is the probability that a random sample of n=400 will have a sample mean more than \$20 greater than the population mean? 5. What is the advantage of the larger sample size? By CLT: x ~ N(754, 227/√100) = N(754, ̅ 22.7) P (x > 774) = 1 ̅ NORM.DIST(774, 754, 22.7, TRUE) = . 1891 By CLT: x ~ N(754, 227/√400) = N(754, ̅ 11.35) P(x > 774) = 1 ̅ NORM.DIST(774, 754, 11.35, TRUE) = . 0390 Example: Homeowner’s insurance 37
Sampling distribution of sample proportion Facts: If sample large enough, Central Limit Theorem applies here, too. What is large enough? np > 5 and n(1-p) > 5 If so, 38 p ˆ ) ) 1 ( , ( ~ ˆ n p p p N p - n p p p p p ) 1 ( ˆ ˆ - = = σ μ

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example: Sampling distribution of proportions The Vice President of sales for Chemicals, Inc. believes that 30% of orders come from new customers. A random sample, n=100, orders is drawn from past orders. 1. Assume the VP is correct. What is the sampling distribution of p̂? 2. What is the probability that the sample proportion, p , ̂ will be less than 0.275? 3. What is the probability that the sample proportion, p̂, will be greater than 0.24? By CLT: p ~ N(0.30, √(.3*.7/100)) = N(0.30, ̂ 0.0458) P(p > .24) = 1- NORMDIST(.24, .30, .0458, TRUE) = ̂ 0.905 P(p < .275) = NORM.DIST(.275, .30, .0458, TRUE) = ̂ 0.293 39
Key learning points: Sampling distributions Means Sampling distribution of sample means has: When population is normally distributed, distribution of sample means is normal regardless of n Central Limit Theorem: When population not normal, if sample size n
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern