Question

Question #1

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

Santa Fe black-on-white is a type of pottery commonly found at archaeological excavations at a certain monument. At one excavation site a sample of 602 potsherds was found, of which 370 were identified as Santa Fe black-on-white. Let p represent the proportion of Santa Fe black-on-white potsherds at the excavation site. Find a point estimate for p. (Round your answer to four decimal places.)

Find a 95% confidence interval for p. (Round your answers to three decimal places.)

lower limit

upper limit

Question # 2

Suppose you are told that a 95% confidence interval for the average price of a gallon of regular gasoline in your state is from $3.03 to $4.15. Use the fact that the confidence interval for the mean is in the form x − E to x + E to compute the sample mean and the maximal margin of error E. (Round your answers to two decimal places.)

x = $

e = $

Question #3

Any state Auto Insurance Company took a random sample of 360 insurance claims paid out during a 1-year period. The average claim paid was $1510. Assume σ = $242. Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

lower limit

upper limit

Find a 0.99 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

lower limit

upper limit

Question #4

Three experiments investigating the relation between need for cognitive closure and persuasion were performed. Part of the study involved administering a "need for closure scale" to a group of students enrolled in an introductory psychology course. The "need for closure scale" has scores ranging from 101 to 201. For the 79 students in the highest quartile of the distribution, the mean score was x = 175.30. Assume a population standard deviation of σ = 8.27. These students were all classified as high on their need for closure. Assume that the 79 students represent a random sample of all students who are classified as high on their need for closure. Find a 95% confidence interval for the population mean score μ on the "need for closure scale" for all students with a high need for closure. (Round your answers to two decimal places.)

lower limit

upper limit

Answer 1

1)

z value at 95% = 1.96

point estimate = 370 / 602 = 0.6146

CI = p +/- z *sqrt(p*(1-p)/n)

= 0.6146 +/- 1.96 *sqrt(0.6146 *(1-0.6146)/602)
= (0.576,0.653)

lower limit = 0.576

upper limit = 0.653

2)

Margin of error
3.03 = x - E ------------1)
4.15 = x + E ................2)

Solving both equations simultaneously,

-2E = -1.12
E = 0.56

3)

z value at 90% = 1.645

CI = 1510 +/- 1.645 *( 242/sqrt(360))
= (1489.02,1530.98)

lower limit =1489.02
upper limit= 1530.98

z value at 99% = 2.576

CI = 1510 +/- 2.576*( 242/sqrt(360))
= (1477.14,1542.86)

lower limit =1477.14
upper limit= 1542.86