The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test at the 0.05 level of significance to see if the mean life spans in the county were the same for whites and nonwhites.a) The null and alternative hypothesis would be: �0:��=��1:��≠�� 0:��=��1:��>�� 0:��=��1:��<�� 0:��=��1:��>�� 0:��=��1:��<�� 0:��=��1:��≠�� b) Determine the test statistic. Round to two decimals.�=c) Find the p-value and compare it to 0.05. Select which is true of the p-value:p = p-value = 0.05 p-value < 0.05 p-value > 0.05 d) Make a decision. Fail to reject the null hypothesis Reject the null hypothesis e) Write the conclusion. There is sufficient evidence to support the claim that whites and nonwhites have different life spans. There is not sufficient evidence to support the claim that whites and nonwhites have different life spans.

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test at the 0.05 level of significance to see if the mean life spans in the county were the same for whites and nonwhites.

a) The null and alternative hypothesis would be:

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b) Determine the test statistic. Round to two decimals.

�=

c) Find the p-value and compare it to 0.05. Select which is true of the p-value:

p =

p-value = 0.05
p-value < 0.05
p-value > 0.05

d) Make a decision.

Fail to reject the null hypothesis
Reject the null hypothesis

e) Write the conclusion.

There is sufficient evidence to support the claim that whites and nonwhites have different life spans.
There is not sufficient evidence to support the claim that whites and nonwhites have different life spans.

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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