The accuracy of a census report on a city in southern California was questioned by some government officials. A random sample of 1215 people living in the city was used to check the report, and the results are shown below.Ethnic OriginCensus PercentSample ResultBlack10% 126 Asian3% 31 Anglo38% 463 Latino/Latina41% 525 Native American6% 58 All others2% 12 Using a 1% level of significance, test the claim that the census distribution and the sample distribution agree.

Name: The accuracy of a census report on a city in southern California was q
Uploaded: 2024-03-20T07:06:27.000Z
Channel: Bartleby
Description: The accuracy of a census report on a city in southern California was questioned by some government officials. A random sample of 1215 people living in the city was used to check the report, and the results are shown below.Ethnic OriginCensus PercentS

The test hypotheses are given below: H0: The census distribution and the sample distribution are same (H0 : pB=0.10; pA=0.03; pA=0.38; pL=0.41; pN=0.06; pA=0.02). H1: The census distribution and the sample distribution are different. The test statistic is calculated by the formula, χ2=∑(O−E)2E Where, O represents the observed frequency and E represents the expected frequency. Methods for finding the expected frequency: Method 1: If the all the expected frequencies are equal, then E=nk Method 2: If the expected frequencies are not equal, then E=np for each category. Where, n is the total number of frequencies, k is the categories and p is the probability of occurrence. Here, the total number of frequencies is 1215 and there are 6 outcomes then k is 6. Also, the probabilities are different. Thus, by using the second method the expected frequencies are calculated as follows. Digits E.frequency E1 121.5 (=(1215)(0.1)) E2 36.45 (=(1215)(0.03) E3 461.7 (=(1215)(0.38)) E4 498.15 (=(1215)(0.41)) E5 72.9 (=(1215)(0.06)) E6 24.3 (=(1215)(0.02)) Ethnic origin Observed Expected Residual (O-E)^2/E Frequency Frequency Black 126 121.5 0.1667 Asian 31 36.45 0.8149 Anglo 463 461.7 0.0037 Latino 525 498.15 1.4472 Native American 58 72.9 3.0454 All others 12 24.3 6.2259Thus, the test-statistic value, χ2 is 11.7037 (=0.1667+0.8149+…+6.2259). P-value: The P-value of the sample statistic is obtained using Excel formula. From EXCEL formula “=CHISQ.DIST.RT(11.7037, 5)”, the P-value is 0.039. Decision rule: If the P-value is less that the significance level, reject the null hypothesis. Otherwise fail to reject the null hypothesis. Conclusion: Here, the P-value is greater that the significance level (=1%). Therefore, by the decision rule, fail to reject the null hypothesis. There is no evidence to conclude that the census distribution and the sample distribution are different.