BAD 2323 Ch8 Hwk CONFIDENCE INTERVALS 1. A study is made to determine how much was spent for a product. A sample of 1,000 people was taken. The sample mean was $300 and the sample standard deviation was $90. Calculate: a. the 68.3% confidence interval b. the 95.4% confidence interval c. the 99.7% confidence interval. 2. A sample of 400 names is taken from a population of 10,000 names. The sample mean is 34.8 years of age. The sample standard deviation is 10.8 years. Calculate the 68.3% confidence interval. 3. A sample of 400 employees is taken from a population of 20,000. The employees were asked if they knew about a certain company policy. In the sample, 30% responded that they did not know. Calculate the 68.3% confidence interval. 4. A sample of 15 employees was taken regarding training days. The sample mean was 53.87 days, while the standard deviation was 6.82 days. Calculate the 95% two sided confidence interval ( t test). 5. A sample of 1,000 was taken to estimate the average expenditure. The sample mean = 520, while the sample std dev = 156. Calculate the 90 % confidence interval. 6. A sample of 200 was taken. The sample mean = 350. The sample std dev = 45. Calculate the 95% confidence interval. 7. A sample of 500 was taken. The sample mean = 2700. The sample std dev = 400. Calculate the 99% confidence interval. 8. The boss wants to know the interval estimate of the average training time required to train employees for a certain task. A sample of n=15 employees was taken. The sample mean = 53.87 minutes with a sample standard deviation of 6.82 minutes. Calculate the 2 tail T test and an alpha risk of 5% ( 95% confidence interval) around the sample mean. 9. For a t distribution with sample size of n = 13, find the area that is in each region? T table uses n - 1 degrees of freedom ( 13 - 1 ) = 12 dof a. b. c. d. e. f. To the left of 1.782 To the right of -1.356 To the right of 2.681 To the left of -1.782 Between -2.170 and +2.179 Between -1.356 and +1.782 10. A sample is composed of the following values: x 5 6 8 10 11 12 13 15 a. What is the point estimate of m ? b. what is the point estimate of s ? c. What is the 95% confidence interval for the population mean? d. What is the 90% confidence interval? 11. Calculate the sample size needed for a 95% confidence interval with a margin of error of 5 and s= 5 12. Calculate the sample size needed for: a. 95% confidence interval with a margin of error of 3 and s= 9 b. 95% confidence interval with a margin of error of 2 and s= 9 13. Calculate the sample size needed for: a. 95% confidence interval with a margin of error of 1.5 and s= 6.82 b. 90% confidence interval with a margin of error of 1.5 and s= 6.82 14. A polling firm takes a survey for a candidate. Let p = .55 a. What is the sample required for 80% confidence interval with margin for error of + - .02? b. What is the sample required for 80% confidence interval with margin for error of + - .04? 1. xx =300, S=90, n=1000 a. =0.315 90 1000 CI=3001.005 3002.86 (297.14, 302.86) b. =0.046 CI=3001.9954 90 1000 3005.68 (294.32, 305.68) c. =0.003 CI=3002.9677 90 1000 3008.45 (291.55, 308.45) 2. n=400, N=10000, S=10.88, xx =34.8 S N n 2 CI= xx t * N 1 n 10.8 10000400 34.8 1.006 400 * 100001 34.80.522 (34.28, 35.32) 3. n=400, N=20,000, p=0.3 CI=0.31.0006 0.30.023 (0.277, 0.323) 0.30.7 20000400 400 200001 4. n=15, xx =53.87, S=6.82, =0.05 d.f=15-1=14 xx tS n 6.82 CI=53.87 2.2010* 15 53.873.88 (49.99, 57.75) 5. n=100, xx =520, S=156, =0.1 5201.645 156 1000 5208.12 (511.88, 528.12) 6. n-200, xx =350, S=45,=0.05 3501.96 45 2 00 3506.24 (343.76, 356.24) 7. n=500, xx =2700, S=400, =0.01 27002.5758* 400 500 270046.08 (2653.92, 2746.08) 8. n=15, xx =53.87, S=6.82, =0.05 D.f=15-1=14 tS xx n 53.87