You are a data analyst for a health insurance company and want to estimate the population mean of the surgery durations for all brain tumor patients. To do so, you select a random sample of 32 brain tumor surgery patients, and you record the surgery duration for each. Assume it is known that the population standard deviation of the durations of all brain tumor surgeries is 1.68 hours. Based on your sample, follow the steps below to construct a 95% confidence interval for the population mean of the surgery durations for all brain tumor patients. (If necessary, consult a list of formulas.) (a)Click on "Take Sample" to see the results from your random sample of 32 brain tumor patients. Take Sample Number of patients Sample mean Sample standard deviation 32 3.54 1.33 Population standard deviation 1.68 Enter the values of the sample size, the point estimate for the population mean, the population standard deviation, and the critical value you need for your 95% confidence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select "Compute". Based on your sample, enter the lower and upper limits to graph the 95% confidence interval for the population mean of the surgery durations for all brain tumor patients.

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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You are a data analyst for a health insurance company and want to estimate the population mean of the surgery durations for all brain tumor patients. To do so, you select a random sample of

brain tumor surgery patients, and you record the surgery duration for each. Assume it is known that the population standard deviation of the durations of all brain tumor surgeries is

1.68

hours.

Based on your sample, follow the steps below to construct a

95%

confidence interval for the population mean of the surgery durations for all brain tumor patients. (If necessary, consult a list of formulas.)

(a)Click on "Take Sample" to see the results from your random sample of

brain tumor patients.

Take Sample

Number of patients	Sample mean	Sample standard deviation
32	3.54	1.33

Population standard deviation
1.68

Enter the values of the sample size, the point estimate for the population mean, the population standard deviation, and the critical value you need for your

95%

confidence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select "Compute".

Based on your sample, enter the lower and upper limits to graph the

95%

confidence interval for the population mean of the surgery durations for all brain tumor patients.

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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