We have the survey data on the body mass index (BMI) of 644 young women. The mea

Question

We have the survey data on the body mass index (BMI) of 644 young women. The mean BMI in the sample was x¯=27.9. We treated these data as an SRS from a Normally distributed population with standard deviation =7.3.

Give confidence intervals for the mean BMI and the margins of error for 90%, 95%, and 99% confidence.

Conf. Level Interval (±0.01)

margins of error (±0.0001)

90%- Confidence interval - margin of error-

95%-Confidence interval- margin of error-

99%-Confidence interval margin of error-

Thank you!

Explanation / Answer

We have the survey data on the body mass index (BMI) of 644 young women. The mean BMI in the sample was x¯=27.9. We treated these data as an SRS from a Normally distributed population with standard deviation =7.3.

Give confidence intervals for the mean BMI and the margins of error for 90%, 95%, and 99% confidence.

Conf. Level Interval (±0.01)

margins of error (±0.0001)

90%- Confidence interval - margin of error-

Confidence Interval Estimate for the Mean

Data

Population Standard Deviation

7.3

Sample Mean

27.9

Sample Size

644

Confidence Level

90%

Intermediate Calculations

Standard Error of the Mean

0.2877

Z Value

1.645

margin of error

0.4732

Confidence Interval

Interval Lower Limit

27.43

Interval Upper Limit

28.37

95%-Confidence interval- margin of error-

Confidence Interval Estimate for the Mean

Data

Population Standard Deviation

7.3

Sample Mean

27.9

Sample Size

644

Confidence Level

95%

Intermediate Calculations

Standard Error of the Mean

0.2877

Z Value

1.9600

margin of error

0.5638

Confidence Interval

Interval Lower Limit

27.34

Interval Upper Limit

28.46

99%-Confidence interval margin of error-

Confidence Interval Estimate for the Mean

Data

Population Standard Deviation

7.3

Sample Mean

27.9

Sample Size

644

Confidence Level

99%

Intermediate Calculations

Standard Error of the Mean

0.2877

Z Value

2.576

margin of error

0.7410

Confidence Interval

Interval Lower Limit

27.16

Interval Upper Limit

28.64

Confidence Interval Estimate for the Mean

Data

Population Standard Deviation

7.3

Sample Mean

27.9

Sample Size

644

Confidence Level

90%

Intermediate Calculations

Standard Error of the Mean

0.2877

Z Value

1.645

margin of error

0.4732

Confidence Interval

Interval Lower Limit

27.43

Interval Upper Limit

28.37

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