In a study on infants, one of the characteristics measured was head circumferenc

Question

In a study on infants, one of the characteristics measured was head circumference. The mean head circumference of 11 infants was 34.6 centimeters (cm). Complete parts through below. Assuming that head circumferences for infants are normally distributed with standard deviation 2.5 cm, determine a 95% confidence interval for the mean head circumference of all infants. The confidence interval for the mean head circumference of all infants is from Obtain the margin of error, E, for the confidence interval you found in part The margin of error is (Round to one decimal place as needed.) 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.) We can be 95% confident that the estimate of mu by x is cm. We can be 95% confident that the error made in estimating mu by x is at least cm. We can be 95% confident that the error made in estimating mu by x is at most cm.

Explanation / Answer

a.) = 2.5; µ = 34.6; n = 11; = 0.05

Margin of Error = z*/n = z/2 * 2.5 / 11

z/2 = 1.96

E = 1.96*2.5/ 11 = 1.477

Confidence Interval = [µ ± E] = [33.12, 36.07]

b.) We have calculated this in previous part, E = 1.477 cm

c.) C. We can be 95% confident that the error made in estimating µ by x-bar is at most 1.477 cm.

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