We have the age distribution in percentages for the whole United States accordin

Question

We have the age distribution in percentages for the whole United States according to the 2010 US Census in the following table. Besides, we have the age distribution in individuals for a simple random sample of 4500 New Yorkers in 2010. At alpha = 0.03, you will need to test if the New York sample's age distribution is the same as the U.S. overall age distribution in 2010. Form the null and alternative hypotheses H_0 and H_1. Make a sketch of the test. Specify appropriate equations for the X^2 statistic and degrees of freedom df. Based on the U.S. overall age distribution, calculate expected frequencies. Given the expected and observed frequencies, calculate the X^2 statistic and its df. Given alpha = 0.03 and df, use CHlSQ.lNV(*, *) to look up for the critical value X^2*. Compare X^2 statistic with X^2* critical to reject or accept H_0. Interpret your result. Sketch and find the p-value of the test. Comment on the p-value and its implication.

Explanation / Answer

(a) H0: both populations distributions are similar

Ha: both populations distributions are not similar

(b) Chi-sq= Sum of (O-E)^2/E & df= n-1=17

(c) Frequency in below table.

(d) frequncies mentioned below

Chi-sq=

df=18-1=17

(e)

(f) observed chi-sq< critical value so cant reject H0. no difference between 2.

(g) P-value=

cant reject H0. no difference between 2.

Solution:

Formula:

10.673503

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