Question

In: Statistics and Probability

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  

Solutions

Expert Solution

a)

95% confidence interval for is

- Z * / sqrt(n) < < + Z * / sqrt(n)

80 - 1.96 * 5 / sqrt(60) < < 80 + 1.96 * 5 / sqrt(60)

78.73 < < 81.27

95% CI is ( 78.73 to 81.27 )

b)

95% confidence interval for is

- Z * / sqrt(n) < < + Z * / sqrt(n)

80 - 1.96 * 5 / sqrt(120) < < 80 + 1.96 * 5 / sqrt(120)

79.11 < < 80.89

90% CI is ( 79.11 to 80.89 )


Related Solutions

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 15. At 95% confidence, what is the margin of error (to 4 decimals)? - What is the standard error of the mean (to 4 decimals)? - Which statement should you use to explain the 95% confidence interval ? Group of answer choices: A. We are confident that 95% of population are in the confidence interval B. We are 95% confident that...
A simple random sample of 80 items resulted in a sample mean of 60. The population...
A simple random sample of 80 items resulted in a sample mean of 60. 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 160 items. Provide a 95% confidence interval for the population mean. (Round your answers to two decimal places.) ___ to ____ c.What is the effect of a...
A simple random sample of 40 items resulted in a sample mean of 80. The population...
A simple random sample of 40 items resulted in a sample mean of 80. The population standard deviation is s=20. a. Compute the 95% confidence interval for the population mean. Round your answers to one decimal place. 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. c. What is the effect of a larger sample size on the...
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 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 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 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). (  ,   )
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT