The U.S. Center for Disease Control reports that in year 1900, the mean life expectancy is 47.6 years for whites and 33 years for nonwhites. (Click here for reference data) Suppose a survey of randomly selected death records for white and nonwhite people born in 1900 from a certain county is conducted. Of the 110 whites surveyed, the mean life span was 48.2 years with a standard deviation of 11.2 years and of the 95 nonwhites, the mean life span was 39.3 years with a standard deviation of 16 years. Conduct a hypothesis test at the 0.05 level of significance to determine whether there was no difference in mean life spans in the county for whites and nonwhites in year 1900. Preliminary: Is it safe to assume that nw≤5% of all white people born in 1900 and nnw≤5% of all nonwhite people born in 1900? No Yes Is nw≥30 and nnw≥30 ? No Yes Test the claim: Determine the null and alternative hypotheses. H0: μw μnw Ha: μw μnw Determine the test statistic. Round to four decimal places. t= Find the p-value. Round to 4 decimals. p-value = Make a decision. Fail to reject the null hypothesis. Reject the null hypothesis. Write the conclusion. There is sufficient evidence to support the claim that whites and nonwhites have different mean life spans. There is not sufficient evidence to support the claim that whites and nonwhites have different mean life spans.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The U.S. Center for Disease Control reports that in year 1900, the mean life expectancy is 47.6 years for whites and 33 years for nonwhites. (Click here for reference data) Suppose a survey of randomly selected death records for white and nonwhite people born in 1900 from a certain county is conducted. Of the 110 whites surveyed, the mean life span was 48.2 years with a standard deviation of 11.2 years and of the 95 nonwhites, the mean life span was 39.3 years with a standard deviation of 16 years. Conduct a hypothesis test at the 0.05 level of significance to determine whether there was no difference in mean life spans in the county for whites and nonwhites in year 1900.

Preliminary:

Is it safe to assume that

nw≤5% of all white people born in 1900 and
nnw≤5% of all nonwhite people born in 1900?
- No
- Yes
Is nw≥30 and nnw≥30 ?
- No
- Yes

Test the claim:

Determine the null and alternative hypotheses.

H0: μw μnw
Ha: μw μnw
Determine the test statistic. Round to four decimal places.
t=
Find the p-value. Round to 4 decimals.
p-value =
Make a decision.
- Fail to reject the null hypothesis.
- Reject the null hypothesis.
Write the conclusion.
- There is sufficient evidence to support the claim that whites and nonwhites have different mean life spans.
- There is not sufficient evidence to support the claim that whites and nonwhites have different mean 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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