Question

In: Statistics and Probability

A simple random sample of 60 items resulted in a sample mean of 65. The population...

A simple random sample of 60 items resulted in a sample mean of 65. The population standard deviation is 16. a. Compute the 95% confidence interval for the population mean (to 1 decimal). ( , ) b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals). ( , ) c. What is the effect of a larger sample size on the margin of error?

3 diff Answers

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 65

Population standard deviation = = 16

Sample size = n = 60

Z/2 = 1.96

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

= 1.96 * (16 / 60)

= 4.05

At 95% confidence interval estimate of the population mean is,

- E < < + E

65 - 4.05 < < 65 + 4.05

60.95 < < 69.05

( 60.95 , 69.05)

Sample size = n = 60

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

= 1.96 * (16 / 120)

= 2.86

At 95% confidence interval estimate of the population mean is,

- E < < + E

65 - 2.86 < < 65 + 2.86

62.14 < < 67.86

( 62.14 , 67.86)

the effect of a larger sample size on the margin of error will decreases


Related Solutions

A simple random sample of 60 items resulted in a sample mean of 65. The population...
A simple random sample of 60 items resulted in a sample mean of 65. The population standard deviation is 16. a. Compute the 95% confidence interval for the population mean (to 1 decimal). ( , ) b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals). ( , ) c. What is the effect of a larger sample size on the margin of...
A simple random sample of 70 items resulted in a sample mean of 60. The population...
A simple random sample of 70 items resulted in a sample mean of 60. The population standard deviation is σ = 15. (a) Compute the 95% confidence interval for the population mean. (Round your answers to two decimal places.) _________ to _________ (b) Assume that the same sample mean was obtained from a sample of 140 items. Provide a 95% confidence interval for the population mean. (Round your answers to two decimal places.) _________ to _________ (c) What is the...
A simple random sample of 60 items resulted in a sample mean of 80. The population...
A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is σ = 5. (a) Compute the 95% confidence interval for the population mean. (Round your answers to two decimal places.)   to   (b) Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean. (Round your answers to two decimal places.)   to  
A simple random sample of 60 items resulted in a sample mean of 80. The population...
A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is σ = 5. (a) Compute the 95% confidence interval for the population mean. (Round your answers to two decimal places.)   to   (b) Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean. (Round your answers to two decimal places.)   to  
A simple random sample of 60 items resulted in a sample mean of 95. The population...
A simple random sample of 60 items resulted in a sample mean of 95. The population standard deviation is 13. a. Compute the 95% confidence interval for the population mean (to 1 decimal). (  ,  ) b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals). (  ,  ) c. What is the effect of a larger sample size on the margin of error? SelectIt increasesIt decreasesIt...
A simple random sample of 60 items resulted in a sample mean of 10. The population...
A simple random sample of 60 items resulted in a sample mean of 10. The population standard deviation is 20. Compute the 95% confidence interval for the population mean. Round to 1 decimal place. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean. Round to 2 decimal places. What is the effect of a larger sample size on the interval estimate? Larger sample provides a larger...
A simple random sample of 60 items resulted in a sample mean of 63. The population...
A simple random sample of 60 items resulted in a sample mean of 63. The population standard deviation is 12. a. Compute the 95% confidence interval for the population mean (to 1 decimal). (  ,   ) b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals). (  ,   )
A simple random sample of 60 items resulted in a sample mean of 89. The population...
A simple random sample of 60 items resulted in a sample mean of 89. The population standard deviation is 18. a. Compute the 95% confidence interval for the population mean (to 1 decimal). ( , ) b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals). ( , ) c. What is the effect of the larger sample size on the margin of...
A simple random sample of 60 items resulted in a sample mean of 67. The population...
A simple random sample of 60 items resulted in a sample mean of 67. The population standard deviation is 12. a. Compute the 95% confidence interval for the population mean (to 1 decimal). (  ,  ) b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals). (  ,  ) c. What is the effect of a larger sample size on the margin of error?
A simple random sample of 60 items resulted in a sample mean of 87. The population...
A simple random sample of 60 items resulted in a sample mean of 87. The population standard deviation is 17. a. Compute the 95% confidence interval for the population mean (to 1 decimal). ( ,  ) b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals). ( , )
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT