Sigicance Tevc 13.23 Distribution: 0.5, 0.3, 0.2 Observed frequencies: 147, 115,

Question

Sigicance Tevc 13.23 Distribution: 0.5, 0.3, 0.2 Observed frequencies: 147, 115, 88 Significance level = 0.01 Applying the Concepts and Skills In each of Exercises 13.24-13.33, apply the chi-square goodness-of- fit test, using either the critical-value approach or the P-value ap- proach, to perform the required hypothesis test. 13.24 Population by Region. According to the U.S. Census Bureau of the U.S. resident population by region in 2000 was as follows. publication Demographic Profiles, a relative-frequency distribution Region Northeast Midwest SouthWest Rel. freq.0.190 0.229 0.356 0.225 A simple random sample of this year's U.S. residents gave the fol- lowing frequency distribution. RegionNortheast Midwest South West Frequency259 306 568 367 a. Identify the population and variable under consideration here. b. At the 5% significance level, do the data provide sufficient evi- dence to conclude that this year's resident population distribution by region has changed from the 2000 distribution?

Explanation / Answer

a) Given data is US resident population by regrion in 2000
Here population is US Residents
b) H0: The resident population distribution by region has not changed from 2000 distribution
H1: The resident population distribution by region has changed from 2000 distribution
Let the los be alpha = 5%

Num Categories: 4
Degrees of freedom: 3

Test Statistic, X^2: 11.2091
Critical X^2: 7.814736
P-Value: 0.0106

Here P-value < alpha 0.05, so we reject H0

The resident population distribution by region has changed from 2000 distribution

Observed Expected Day freq (Oi) Probability (Ei) (Oi-Ei)^2/Ei Northeast 259 0.19 285 2.371929825 Midwest 306 0.229 343.5 4.093886463 South 568 0.356 534 2.164794007 West 367 0.225 337.5 2.578518519 Total := 1500 11.20912881

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