In response to the statement “An effective leader must be able to feel the emotions of his group-members,”

the response categories (Strongly agree, Agree, Disagree, Strongly disagree) had counts (103, 375, 425, 97) for responses in an Emotional Quotient Survey. To treat this ordinal variable as quantitative, we assign scores to the categories. For the scores (2, 1, −1, −2), which treat the distance between Agree and Disagree as twice the distance between Strongly agree and Agree or between Disagree and Strongly disagree, software reports

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n Mean Std Dev Std Err 1000 -.048 1.543 0.0413

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(a) Set up null and alternative hypotheses to test whether the population mean response differs from the neutral value, 0.

(b) Find the test statistic and P-value. Interpret, and make a decision about H0, using α = 0.05.

(c) Based on (b), can you “accept” H0: μ = 0? Why or why not?

(d) Construct a 95% confidence interval for μ. Show the correspondence between whether 0 falls in the interval and the decision about H0.