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An expert witness in a case of alleged racial discrimination in a state university school of nursing introduced a regression of the determinants of Salary of each professor for each year during an 8-year period (n = 423) with the following results, with dependent variable Year (year in which the salary was observed) and predictors YearHire (year when the individual was hired), Race (1 if individual is black, 0 otherwise), and Rank (1 if individual is an assistant professor, 0 otherwise). Interpret these results.

Variable Coefficient t p
Intercept -3,816,521 -29.4 .000
Year 1,948 29.8 .000
Year Hire -826 -5.5 .000
Race -2,093 -4.3 .000
Rank -6,438 -22.3 .000
R2 = 0.811 R2adj = 0.809 s = 3,318

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The regression equation can be written as:
Salary = -3816521 + 1948 * Year – 826 * Year Hire – 2093 * Race – 6438 * Rank
This implies that the Salary is increasing with the year, but ...

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Step-wise answer to Testing of hypothesis problems

A decade-old study found that the proportion, p, of high school seniors who believed that "getting rich" was an important personal goal was 75%. A researcher decides to test whether or not that percentage still stands. He finds that, among the 250 high school seniors in his random sample, 182 believe that "getting rich" is an important goal. Can he conclude, at the 0.05 level of significance, that the proportion has indeed changed?
Perform a two-tailed test. Then fill in the table below.

The null hypothesis is:
The alternative hypothesis is:

The type of test statistic is: z, t, chi square or f

The value of the test statistic is (round to at least three decimals)

The two critical values at the 0.05 level of significance (round to at least three decimals)

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