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# 1. A university researcher is interested in whether efforts to recruit more top high school students...

1. A university researcher is interested in whether efforts to recruit more top high school students have been successful. To test this, she randomly selects 50 freshmen from the university and records their high school GPA. The mean is 2.75 with a standard deviation of 0.50. The researcher also knows that the mean high school GPA of all freshmen enrolled at the university five years ago was 3.00 with a standard deviation of 0.66. The researcher wants to know if the high school GPA of current freshman at the university is better than that of freshman from five years ago.

(a) What are the null and alternative hypotheses in this study (stated mathematically)?

(b) Should the researcher use a one-tailed or a two-tailed test?

(c) Compute the appropriate test statistic for testing the hypothesis.

(d) Using α = 0.05, what do you conclude about the high school GPA of current freshman? Be sure to include a discussion of the critical value in your answer.

(e) What type of error might the researcher be making in part (d)?

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