The U.S. Center for Disease Control reports that in year 1900, the mean life expectancy is 48 years for whites and 46.9 years for nonwhites with a stanard deviation of 11.1 years and the nonwhites had a stanard deviation of 15.6 years. Suppose the representative populations were 29,000 whites and 96,000 nonwhites. Conduct a hypothesis test at the 0.1 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 nw≥30 and nnw≥30 ?YesNo Test the claim:Determine the null and alternative hypotheses. H0H0: μw μnw HaHa: μw μnwDetermine the test statistic. Round to four decimal places.z=Find the pp-value. Round to 4 decimals.pp-value = Make a decision.Reject the null hypothesis.Fail to reject the null hypothesis.Write the conclusion.There is not sufficient evidence to support the claim that whites and nonwhites have different mean life spans.There is sufficient evidence to support the claim that whites and nonwhites have different mean life spans.

Solution: Given information: n1= 29000 Sample size of white population n2= 96000 Sample size of nonwhite population x1= 48 Sample mean of white population x2= 46.9 Sample mean of nonwhite population s1=11.1 Sample standard deviation of white popuation s2= 15.6 Sample standard deviation of nonwhite popuation α= 0.10 Level of significance Yes w≥30 and nw≥30 Yes option A is Correct 1) The null and alternative hypothesis is Ho:μw= μnwVS Ha::μw≠ μnw 2) Test statistic z= x1-x2s12n1+s22n2z =48-46.911.1229000+15.6296000z =48-46.9123.2129000+243.3696000z=48-46.90.004249+0.002535z=48-46.90.006784z=1.10.082365=13.355187z= 13.3552 Test statistic z = 13.3552 3) To find p value P value = 2*P( Z> 13.3552) P value = 0.0000 From Excel 4) Decision: P value < α=0.10 Reject the null hypothesis. Option A is Correct 5) Conclusion: There is sufficient evidence to support the claim that whites and nonwhites have different mean life spans. Option B is Correct

Answered: The U.S. Center for Disease Control…

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 48 years for whites and 46.9 years for nonwhites with a stanard deviation of 11.1 years and the nonwhites had a stanard deviation of 15.6 years. Suppose the representative populations were 29,000 whites and 96,000 nonwhites. Conduct a hypothesis test at the 0.1 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 nw≥30 and nnw≥30 ?

Test the claim:

Determine the null and alternative hypotheses.

H0H0: μw μnw
HaHa: μw μnw
Determine the test statistic. Round to four decimal places.
z=
Find the pp-value. Round to 4 decimals.
pp-value =
Make a decision.
- Reject the null hypothesis.
- Fail to reject the null hypothesis.
Write the conclusion.
- There is not sufficient evidence to support the claim that whites and nonwhites have different mean life spans.
- There is 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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