A medical research team at the university is investigating the effectiveness of a new medical treatment for a rare disease. Data indicates that under the current treatment, patients have a mean white blood cell count of 23 cells/cc (cubic centimeter). This distribution is understood to be normally distributed, but the population standard deviation is not known. The new treatment will only be deemed effective if it significantly increases the patient’s white blood cell count above 23 cells/cc. The team has applied the treatment to a random sample of 10 patients. They have reported the following blood cell counts:21, 25, 18, 24, 19, 25, 22, 20, 27, 25 At α = .01, is the new treatment effective?

It is given that the new treatment will only be deemed effective if it significantly increases the…

Answered: A medical research team at the…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 22SGR

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A medical research team at the university is investigating the effectiveness of a new medical treatment for a rare disease. Data indicates that under the current treatment, patients have a mean white blood cell count of 23 cells/cc (cubic centimeter). This distribution is understood to be normally distributed, but the population standard deviation is not known. The new treatment will only be deemed effective if it significantly increases the patient’s white blood cell count above 23 cells/cc.

The team has applied the treatment to a random sample of 10 patients. They have reported the following blood cell counts:

21, 25, 18, 24, 19, 25, 22, 20, 27, 25

At α = .01, is the new treatment effective?

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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