Question

Consider a population with a known standard deviation of 15.3. In order to compute an interval estimate for the population mean, a sample of 41 observations is drawn. [You may find it useful to reference the z table.]

a. Is the condition that X−X−  is normally distributed satisfied? choose one of the following

• Yes

• No

b. Compute the margin of error at a 99% confidence level. (Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and final answer to 2 decimal places.)

margin of error: ______

c. Compute the margin of error at a 99% confidence level based on a larger sample of 340 observations. (Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and final answer to 2 decimal places.)

margin of error:_____

d. Which of the two margins of error will lead to a wider confidence interval? choose one of the following.

• 99% confidence with n = 340.

• 99% confidence with n = 41.

Answer 1

Consider a population with a known standard deviation of 15.3. In order to compute an interval estimate for the population mean, a sample of 41 observations is drawn. [You may find it useful to reference the z table.]

a. Is the condition that X−X−  is normally distributed satisfied? choose one of the following

Correct option: Yes

No

( note: sample size is large (>30)) .

b. Compute the margin of error at a 99% confidence level. (Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and final answer to 2 decimal places.)

margin of error: ______

for 99% level z= 2.576

margin of error = z*sd/sqrt(n) = 2.576*15.3/sqrt(41) = 6.155245

= 6.16 ( two decimals)

c. Compute the margin of error at a 99% confidence level based on a larger sample of 340 observations. (Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and final answer to 2 decimal places.)

margin of error:_____

margin of error = z*sd/sqrt(n) = 2.576*15.3/sqrt(340) = 2.137459

=2.14 ( two decimals)

d. Which of the two margins of error will lead to a wider confidence interval? choose one of the following.

99% confidence with n = 340.

Correct option: 99% confidence with n = 41.