In a study on infants, one of the characteristics measured was head circumference. The mean head circumference of 8 infants was 34.2 centimeters(cm). Complete parts(a) through(d) below.

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Click here to view Page 2 of the table of areas under the standard normal curve. a. Assuming that head circumferences for infants are normally distributed with standard deviation 2.4cm, determine a 90% confidence interval for the mean head circumference of all infants.

The confidence interval for the mean head circumference of all infants is from

enter your response here cm to

enter your response here cm.(Round to one decimal place as needed.)

Part 2

b. Obtain the margin of error, E, for the confidence interval you found in part(a).

The margin of error is

enter your response here cm.

(Round to one decimal place as needed.)

Part 3

c. Explain the meaning of E in this context in terms of the accuracy of the estimate. Choose the correct answer below and fill in the answer box to complete your choice.

(Round to one decimal place as needed.)

A.

We can be 90% confident that the error made in estimating mu by x overbar is at most

enter your response here cm.

B.

We can be 90% confident that the possible values of mu are within

enter your response here cm of each other.

C.

We can be 90% confident that the estimate of mu by x overbar is

enter your response here cm.

D.

We can be 90% confident that the error made in estimating mu by x overbar is at least

enter your response here cm.

Part 4

d. Determine the sample size required to have a margin of error of 0.8 cm with a 95% confidence level.

The required sample size is

enter your response here. (Round up to the nearest whole number.)