Question

In: Statistics and Probability

Given the following information: the sample size n = 20, the sample mean= 75.3, and the...

Given the following information: the sample size n = 20, the sample mean= 75.3, and the population standard deviation= 6.0. Please show your work. Find the 0.99 confidence interval for

Solutions

Expert Solution

Solution :

Given that,

= 75.3

= 6.0

n = 20

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576

Margin of error = E = Z/2* ( /n)

= 2.576 * (6 / 20)

= 3.5

At 99% confidence interval estimate of the population mean is,

- E < < + E

75.3 - 3.5 < < 75.3 + 3.5

71.8 < < 78.8

(71.8 , 78.8 )

orchestra answered 1 year ago
Next > < Previous

Related Solutions

Suppose you have a sample size of n = 20, with a sample mean of 65...
Suppose you have a sample size of n = 20, with a sample mean of 65 and a sample standard deviation of 15. Suppose the population mean is thought to be 50. You want to find out whether your sample mean is different from the population mean. Which test should you use? Select one: a. paired t-test b. two proportion z-test c. one proportion z-test d. two sample t-test e. one sample t-test.
Given a variable with the following population parameters: Mean = 20 Variance = 16 Sample Size...
Given a variable with the following population parameters: Mean = 20 Variance = 16 Sample Size = 35 a) What is the probability of obtaining a mean greater the 23? b) What is the probability of obtaining a mean less than 21? c) What is the probability of obtaining a mean less than 18.2? d) What is the probability of obtaining a mean greater than 19.5 and less than 21.2? e) What is the probability of obtaining a mean greater...
Country Sample Size Sample Mean Sample Standard Deviation UK n=20 X1= 8.39 S1= 0.035347565 Turkey n=20...
Country Sample Size Sample Mean Sample Standard Deviation UK n=20 X1= 8.39 S1= 0.035347565 Turkey n=20 X2= 1.88 S2= 0.005744989 a) Test at 5% level individually if the mean percentage for each of the countries is different from 10%. b)   Obtain a 95% confidence interval for the difference of means for the two countries. c) Test an appropriate pair of hypotheses for the two means at 5% level of significance. d)   For each country test at 5% level if the...
Given a linear correlation coefficient r = 0.476, a sample size n = 20, and a...
Given a linear correlation coefficient r = 0.476, a sample size n = 20, and a significance level of α = 0.05, use Table A-6 to determine the critical value of r and state if the given r represents a significant linear correlation. Would your answer change if the significance level was α = 0.01?
Assume a study of sample size n was conducted and the sample mean was found to...
Assume a study of sample size n was conducted and the sample mean was found to be  and the sample variance s2. Which of the below is the correct way to calculate the standard error of the mean of the sample? Suppose you found the prices for 11 recently sold puppies in your area and recorded them in the table below. The next few questions will use this sample. Price ($): 1437.78 1902.35 1657.76 2057.27 1823.35 1816.12 1808.84 1654.00 1815.81 1968.85...
A simple random sample of size n is drawn. The sample​ mean is found to be...
A simple random sample of size n is drawn. The sample​ mean is found to be 17.6​, and the sample standard​ deviation, s, is found to be 4.7. A). Construct a 95​% confidence interval about if the sample​ size, n, is 51.
A simple random sample of size n is drawn. The sample​ mean is found to be...
A simple random sample of size n is drawn. The sample​ mean is found to be 17.6​, and the sample standard​ deviation, s, is found to be 4.7. Construct a 99​% confidence interval about if the sample​ size, n, is 34.
A sample of size 20 yields a sample mean of 23.5 and a sample standard deviation...
A sample of size 20 yields a sample mean of 23.5 and a sample standard deviation of 4.3. Test HO: Mean >_ 25 at alpha = 0.10. HA: Mean < 25. This is a one-tailed test with lower reject region bounded by a negative critical value.
A simple random sample of size n is drawn. The sample​ mean, x​, is found to...
A simple random sample of size n is drawn. The sample​ mean, x​, is found to be 18.5, and the sample standard​ deviation, s, is found to be 4.6. ​(a) Construct a 95​% confidence interval about μ if the sample​ size, n, is 34. Lower​ bound: ___ Upper​ bound: ___ ​(Use ascending order. Round to two decimal places as​ needed.) ​(b) Construct a 95% confidence interval about μ if the sample​ size, n, is 61. Lower​ bound: ___ Upper​ bound:...
A simple random sample of size n is drawn. The sample mean, x, is found to...
A simple random sample of size n is drawn. The sample mean, x, is found to be 35.1, and the sample standard deviation, s, is found to be 8.7 a) Construct a 90% confidence interval for μ if the sample size, n, is 100. b) Construct a 90% confidence interval for μ if the sample size, n, is 40. How does decreasing the sample size affect the margin of error, E? c) Construct a 96% confidence interval for μ if...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT