Bilirubin is a yellowish substance in your blood that forms after red blood cells break down and it travels through your liver, gallbladder, and digestive tract before being excreted. Elevated levels may indicate liver damage as your liver isn’t clearing bilirubin properly. A researcher is interested in estimating the mean Bilirubin level for a population of patients with liver disease along with its 90% confidence interval. The researcher collected data from a sample of 24 patients and found the average Bilirubin level is 86.08 with standard deviation 106. However, due to the skewness in the data, a natural logarithm of the data was performed to satisfy normality assumption required for calculating the confidence interval. The resulted 90% confidence interval for the mean Bilirubin level under the natural log transformation is (3.69,4.3). Which one of the following options best helps the researcher in making inference about the true population mean Bilirubin level? a. Based on the information provided, the researcher can conclude that the true population mean Bilirubin level is more likely to be between 40.04 and 73.7 with 90% confidence level. b. Based on the information provided, the researcher can conclude that the true population mean Bilirubin level is more likely to be between 1.31 and 1.46 with 90% confidence level. c. Based on the information provided, the researcher can conclude that the true population mean Bilirubin level is more likely to be between 3.69 and 4.3 with 90% confidence level. d. Based on the information provided, the researcher can conclude that the true population mean Bilirubin level is more likely to be between 49 and 123.16 with 90% confidence level. e. Based on the information provided, the researcher can conclude that the true population mean Bilirubin level is more likely to be between 50.49 and 121.67 with 90% confidence level.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Bilirubin is a yellowish substance in your blood that forms after red blood cells break down and it travels through your liver, gallbladder, and digestive tract before being excreted. Elevated levels may indicate liver damage as your liver isn’t clearing bilirubin properly.

A researcher is interested in estimating the mean Bilirubin level for a population of patients with liver disease along with its 90% confidence interval.

The researcher collected data from a sample of 24 patients and found the average Bilirubin level is 86.08 with standard deviation 106. However, due to the skewness in the data, a natural logarithm of the data was performed to satisfy normality assumption required for calculating the confidence interval. The resulted 90% confidence interval for the mean Bilirubin level under the natural log transformation is (3.69,4.3).

Which one of the following options best helps the researcher in making inference about the true population mean Bilirubin level?

		a. Based on the information provided, the researcher can conclude that the true population mean Bilirubin level is more likely to be between 40.04 and 73.7 with 90% confidence level.
		b. Based on the information provided, the researcher can conclude that the true population mean Bilirubin level is more likely to be between 1.31 and 1.46 with 90% confidence level.
		c. Based on the information provided, the researcher can conclude that the true population mean Bilirubin level is more likely to be between 3.69 and 4.3 with 90% confidence level.
		d. Based on the information provided, the researcher can conclude that the true population mean Bilirubin level is more likely to be between 49 and 123.16 with 90% confidence level.
		e. Based on the information provided, the researcher can conclude that the true population mean Bilirubin level is more likely to be between 50.49 and 121.67 with 90% confidence level.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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