A trading magazine wants to know if a seminar on self-confidence helps stockbrokers to obtain new clients. Before and after the self-confidence seminar, 14 stockbrokers rated their self-confidence as low, neutral, or high. In comparing the before and after rankings, there was one plus sign and 13 negative signs for the sign test.a. Specify the competing hypotheses to determine if there are differences in self-confidence before and after the seminar.b. Assuming the proportion of plus signs follows a normal distribution, what is the value of the test statistic?c. At the 1% significance level, what is the decision and conclusion?
What will be an ideal response?
a. The competing hypotheses are H0: p ? 0.5; HA: p < 0.5
b. The proportion of plus signs is 
= 0.0714. The test statistic value is z = -3.207.
c. At the 1% significance level, the critical value is -2.576. The p-value is
P(Z ? ?3.207) = 0.0007. Reject the null hypothesis. We can conclude that stockbroker self-confidence is improved by the seminar.
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