ECON 260-03 Statistics for Business and Economics Dominican University Fall 2016-2017 Lawrence Morgan ECON 260 GRADED ASSIGNMENT CHAPTER 7 POINTS: _______ PERCENTAGE: ________ (24 POINTS TOTAL) Name: _____________________________ PUT ANSWERS WITHIN THE BOXES IN EACH QUESTION. SUBMIT THE SPREADSHEET THROUGH CANVAS. IN THE CELLS DO NOT SIMPLY WRITE THE ANSWER BUT PUT IN THE EXCEL FUNCTIONS OR CALCULATIONS SO I CAN SEE WHAT YOU DID TO GET THE ANSWERS.USE THE FORMULAS ON THE FORMULA SHEET. I SUGGEST YOU SKETCH GRAPHS OF THE DISTRIBUTIONS AND WRITE OUT THE FORMULAS IF THAT HELPS TO CLARIFY THE SOLUTION TO YOU. I. 1 Given a sample mean standard deviation II. 2 Given a simple random sample of 250 people from a very large population, you find that 63 of them are Buddhist. Calculate the standard error . (2 points) III. (based on page 325 #15) (4 points) A population has a mean of 173 and a standard deviation of 47. Suppose a simple random sample of size 100 is selected and is used to estimate μ. (first calculate the standard error of the mean 𝜎𝑥ҧ ) 3 What is the probability that the sample mean will be within ±5 of the population mean? 4 IV. What is the probability that the sample mean will be within ±10 of the population (based on page 331, #30) (4 points) ҧ used to The population proportion p 0.41. Supposed a simple random sample of size 200 is selected and 𝑝is estimate p . (first calculate the standard error of the proportion 𝜎𝑝ҧ ) 5 What is the probability that a sample proportion will be within ±0.03 of the population proportion? 6 V. from a sample of 250, and a known population , calculate the standard error . (2 points) What is the probability that a sample proportion will be within ±0.06 of the population proportion? (based on page 338, #40) (6 points) Foot Locker uses sales per square foot as a measure of productivity. Sales are currently at $406 per square foot on average for the entire firm. You take a sample of 64 Foot Locker stores. Assume the standard deviation in annual sales per square foot for the population of 3400 Foot Locker stores is $80. VI. 7 Show the expected value and the standard deviation of 𝑥,ҧ sample mean of this sample. 8 What is the probability that the sample mean will be within $15 of the population mean? 9 Suppose you find a sample mean 𝑥ҧ of $380. What is the probability of finding a sample mean of $380 or less. (based on page 339, #46) (6 points) 15% of Australian smoke. By introducting tough laws banning brand labels on cigarette packages, Australia hopes to reduce the percentage of people who smoke to 10%. Answer the following based on a sample of 240 Australians. 10 Show the expected value and the standard error of the sample proportion 𝑝ҧ . 11 What is the probability that the sample proportion will be within ±0.04 of the population proportion? 12 Suppose you find a sample proportion 𝑝ҧ = 0.16. What is the probability of finding a sample proportion of 0.16 or more?

ECON 260-03 Statistics for Business and Economics Dominican University Fall 2016-2017 Lawrence Morgan FORMULAS: 1. Expected value of sample mean: ̅̅̅ = 𝜇 𝐸(𝑥) 2. Standard error of sample mean: 𝜎𝑥̅ = 3. Expected value of sample proportion: 𝐸(𝑝̅ ) = 𝑝 4. Standard error of sample proportion: 𝜎𝑝̅ ≈ √ 5. z-value: 6. Probability that x is less than or equal to x0 : 𝑃(𝑥 ≤ 𝑥0 ) = NORM.DIST(x,μ,σ,TRUE) 7. Probability that x is greater than or equal to x0 : 𝑃(𝑥 ≥ 𝑥0 ) = 1 − 𝑃(𝑥 ≤ 𝑥0 ) = 1-NORM.DIST(x,μ,σ,TRUE) 8. Probability that x is between x0 and x1 : 𝑃(𝑥0 ≤ 𝑥 ≤ 𝑥1 ) = 𝑃(𝑥 ≤ 𝑥1 ) − 𝑃(𝑥 ≤ 𝑥0 ) = =NORM.DIST(x1,μ,σ,TRUE)-NORM.DIST(x0,μ,σ,TRUE) 9. Probability that z is less than or equal to z0 : 𝑃(𝑧 ≤ 𝑧0 ) = NORM.S.DIST(z0,TRUE) 10. Probability that z is greater than or equal to z0 : 𝑃(𝑧 ≥ 𝑧0 ) = 1 − 𝑃(𝑧 ≤ 𝑧0 ) = 1-NORM.S.DIST(z0,TRUE) 11. Probability that z is between z0 and z1 : 𝑃(𝑧0 ≤ 𝑧 ≤ 𝑧1 ) = 𝑃(𝑧 ≤ 𝑧1 ) − 𝑃(𝑧 ≤ 𝑧0 ) = =NORM.S.DIST(z1,TRUE)-NORM.DIST(z0,TRUE) 𝑧= 𝜎 √𝑛 𝑝(1−𝑝) 𝑛 𝑥−𝜇 𝜎 Page 1 of 1