A researcher studying stress is interested in the blood pressure measurements of chief executive officers (CEOs) of major corporations. He has good reason to believe that the mean systolic blood pressure, mean population, of CEOs of major corporations is less than 134 mm Hg, which is the value reported in a possibly outdated journal article. He plans to perform a statistical test. He measures the systolic blood pressures of a random sample of CEOs of major corporations and finds the mean of the sample to be 128 mm Hg and the standard deviation of the sample to be 20 mm Hg. Based on this information, complete the parts below. (a) What are the null hypothesis and the alternative hypothesis that should be used for the test? (b) Suppose that the researcher decides not to reject the null hypothesis. What sort of error might he be making? (Select one): Type I or Type II (c) Suppose the true mean systolic blood pressure of CEOs of major corporations is 124 mm Hg. Fill in the blanks to describe a Type II error. A Type II error would be (Select one): Rejecting or Failing to reject; the hypothesis that mean population is (Select one): less than/less than or equal to/greater than or equal to/greater than/not equal to/equal to (Select one): 128/134/20 when, in fact, mean population is (Select one): equal to 20/equal to 134/less than 20/less than 134/greater than 128/greater than 134 .

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 2AGP

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A researcher studying stress is interested in the blood pressure measurements of chief executive officers (CEOs) of major corporations. He has good reason to believe that the mean systolic blood pressure, mean population, of CEOs of major corporations is less than 134 mm Hg, which is the value reported in a possibly outdated journal article. He plans to perform a statistical test. He measures the systolic blood pressures of a random sample of CEOs of major corporations and finds the mean of the sample to be 128 mm Hg and the standard deviation of the sample to be 20 mm Hg.
Based on this information, complete the parts below.
(a) What are the null hypothesis and the alternative hypothesis that should be used for the test?

(b) Suppose that the researcher decides not to reject the null hypothesis. What sort of error might he be making? (Select one): Type I or Type II

(c) Suppose the true mean systolic blood pressure of CEOs of major corporations is 124 mm Hg. Fill in the blanks to describe a Type II error.
A Type II error would be (Select one): Rejecting or Failing to reject; the hypothesis that mean population is (Select one): less than/less than or equal to/greater than or equal to/greater than/not equal to/equal to (Select one): 128/134/20 when, in fact, mean population is (Select one): equal to 20/equal to 134/less than 20/less than 134/greater than 128/greater than 134 .

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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