Question

Study 1: Unemployment Rates in Areas Where Minimum Wages Are Higher in the Cities Than in Surrounding Suburbs City Unemployment Rates Suburb Unemployment Rates P1 P 1 = 0.069 P2 P 2 = 0.062 N1 N 1 = 52 cities N2 N 2 = 56 suburbs The Z(obtained) test statistic is 1.99. Using a significance level of .05, the Z(critical) is +1.645. Which of the following is the appropriate conclusion to your hypothesis test? The difference between the unemployment rates in the cities and the suburbs is statistically significant. The difference between the unemployment rates in the cities and the suburbs is not statistically significant. Suppose you conduct a second study and ask half as many people the same question. Suppose the proportions remain approximately the same. The new results are shown in the following table: Study 2: Unemployment Rates in Areas Where Minimum Wages Are Higher in the Cities Than in Surrounding Suburbs City Unemployment Rates Suburb Unemployment Rates P1 P 1 = 0.068 P2 P 2 = 0.061 N1 N 1 = 26 cities N2 N 2 = 28 suburbs When compared with the first study, you would expect the Z(obtained) test statistic to and the Z(critical) to . Without computing the test statistic for the second study, you your conclusion will be the same as your conclusion for the first study. Now that you have a sense of how changing the sample size affects the statistical significance of the statistical finding, what about whether the test is one-tailed or two-tailed? How does moving from a one-tailed test to a two-tailed test change the probability of rejecting the null hypothesis? The probability of rejecting the null hypothesis does not change. The probability of rejecting the null hypothesis decreases. The probability of rejecting the null hypothesis increases. How does changing the sample size, or changing from one-tailed to two, affect the importance of the statistical finding? Check all that apply. Sample size does not affect the importance of a statistical finding. Changing from two-tailed to one is more likely to produce a statistically significant finding, but that doesn't mean it will be more important. A small sample is more likely to result in an important statistical finding. A large sample is more likely to result in an important statistical finding.

Answer 1

Solution

Part (a)

Since the Z(obtained) test statistic (1.99) > the Z(critical) (+1.645), the null hypothesis of no difference is rejected.

So, the answer is: The difference between the unemployment rates in the cities and the suburbs is not statistically significant. Answer 1

Part (b)

Moving from a one-tailed test to a two-tailed test results if a smaller critical value, the significance level remaining the same.

And hence the probability of rejecting the null hypothesis decreases. Answer 2

Part (c)

Effect of changing the sample size, or changing from one-tailed to two, on the importance of the statistical finding

1. Sample size does not affect the importance of a statistical finding.

2. Changing from two-tailed to one is more likely to produce a statistically significant finding, but that doesn't mean it will be more important.

3. A small sample is more likely to result in an important statistical finding.

4. A large sample is more likely to result in an important statistical finding.

(2) and (4) are valid conclusions. (1) and (3) are NOT. Answer 3

DONE