Question

Attempts:Keep the Highests 4. Sample size, statistical significance, and practical importance Cities across the country are passing higher minimum wages, increasing the discrepancy between the wages in the dity and those in the suburbs. Suppose you are interested in the relationship between unemployment duration in the city and the surrounding suburbs in areas where the dites have minimum wages that are at least $3 higher than the minimum wages of the surrounding suburbs. The results are shown in the following table: Study 1: Unemployment Duration in Areas Where Minimum Wages Are Higher in City Unemployment Duration Suburb Unemployment Duration 1 26.6 weeks N70 cities the Citles Than in Surrounding Suburbs X2 29.5 weeks N2 84 suburbs The Z(obtained) test statistic is-2.01. Using a significance level of .05, the Z(critical) is-1.645. Which of the following is the appropriate conclusion to our hypothesis test? O The difference between the unemployment duration in the cities and the suburbs is statistically significant. O The difference between the unemployment duration in the cities and the suburbs is not statistically significant.

Answer 1

As given in the question: The null hypothesis and the alternative hypothesis are given by: H : - = 0 H:14 - Hy >0 (Right tailed test) Pobtained =-2.01 -critical =-1.645 The level of significance a = 0.05 Here, the obtained value of - is less than the critical value of . -2.01 <-1.645 Therefore, reject the null hypothesis at the 0.05 level of significance. Hence, the difference between the unemployment duration in the cities and the suburbs is statistically significant. When completed with the first study, Z(obtained) test statistics to increase and the Z(critical) to remain the same. Without computing the test statistic for the second study, you do not expect your conclusion will be the same as your conclusion for the first study. The p-value of the hypothesis testing for a two-tailed test is twice as the p-value of the hypothesis testing for a one-tailed test. Therefore, moving from a two-tailed test to a one-tailed test will decrease the probability of rejecting the null hypothesis. Changing the sample size will more likely to result in an important statistical finding. And changing from two-tailed to one will produce a statistically significant finding, but that doesn't mean it will be less important. Hence, option (C) and (D) both are correct.