The latest available data showed health expenditures were $8086 per person in th

Question

The latest available data showed health expenditures were $8086 per person in the United States or 17.6% of gross domestic product (Centers for Medicare & Medicaid Services website, April 1, 2012). Use $8086 as the population mean and suppose a survey research firm will take a sample of 100 people to investigate the nature of their health expenditures. Assume the population standard deviation is $2500. a. Show the sampling distribution of the mean amount of health care expenditures for a sample of 100 people. b. What is the probability the sample mean will be within plusminus $200 of the population mean? c. What is the probability the sample mean will be greater than $9000? If the survey research firm reports a sample mean greater than $9000, would you question whether the firm followed correct sampling procedures? Why or why not?

Explanation / Answer

a) here sampling distribution will be normal as n>30

with mean =8086

and std error=std deviation/(n)1/2=250

b)P(8086-200<X<8086+200)=P(-200/250<Z<200/250)=P(-0.8<Z<0.8)=0.7881-0.2119 =0.5763

c) P(X>9000)=1-P(X<9000)=1-P(Z<(9000-8086)/250)=1-P(Z<3.668)=1-0.9999=0.0001

Yes we need to question as probaility of that happening is very less and we may doubt that mean should be greater then 8086

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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