According to the most recent census, 16.3% of US residents are of Hispanic origi

Question

According to the most recent census, 16.3% of US residents are of Hispanic origin. One county supervisor lieves her county has a smaller percentage than what was reported in the census. A survey of 197 individuals in the county was conducted, and each person was asked to report their origin. It was found that 13.26% of those surveyed identified as being of Hispanic origin Test the appropriate hypotheses using a significance level of 0.01. . Ho: Select an answervEv : [Select an answerV] decision rule: reject Ho if probability . Test Statistic: z (Note: round the z-score to two decimal places carry at least four decimal places throughout all of your calculations) probability Decision: Select an answer Conclusion: At the 0.01 level,there Select an answer significant evidence to conclude the (Note: round the probability to four decimal places) percentage of residents in this county who are of Hispanic origin is select an answer 16.3%.

Explanation / Answer

H0: p = 0.163

Ha : p < 0.163

Here = 0.01

Decision rule : reject H0if probability <

Here sample size n = 197

sample proportion p^ = 0.1326

standard error of proportion sep= sqrt [p^ * (1-p^)/n) = sqrt[0.163 * (1 - 0.163)/197] = 0.0263

Test statistic

z = (p^ - p0)/sep = (0.1326 - 0.163)/0.0263 = -1.1552 or -1.16

p- value = Pr(Z < -1.1552) = 0.1240

So here as p - value > 0.01 so we failed to reject the null hypothesis.

Conclusion : at the 0.01 level, there is insufficient evidence to conclude that the percentage of residents in this county of residents in this county who are of Hispanic origin is less than 16.3%.

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