Question

Suppose that in a certain city the proportion of the city’s population that classified themselves as Caucasian in the most recent census was .56. A sociologist believes that the proportion Caucasian residents has changed. To test this claim, the sociologist surveys 130 randomly selected residents of the city; 63 of the individuals surveyed classify themselves as Caucasian. a.Verify that the sample the sociologist obtained satisfies the conditions for inference.b.Does the sociologist have evidence to support their belief?Use ?=0.05.

Answer 1

Solution:

a. Verify that the sample the sociologist obtained satisfies the conditions for inference.

Answer: a. The sample selected is a random sample.

b. The sample size is less than 5% of the population size.

c. and

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b. The null and alternative hypotheses are:

Under the null hypothesis, the test statistic is:

Where:

Conclusion: Since the p-value is greater than the significance level, we, therefore, fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim that the proportion of Caucauan residents has changed at the 0.05 significance level.