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The dean of students of a large private college claims that the average distance commuting students...

The dean of students of a large private college claims that the average distance commuting students travel to the campus is 32 miles. The commuting students feel otherwise. A sample of 64 students was randomly selected and yielded a mean of 35 miles and a standard deviation of 5 miles. Identify the null and alternative hypotheses. Test the dean’s claim at the 5 percent level of significance (α = 0.05) using critical approach and state a conclusion.   

(Hint: two-tailed test, zα/2 = 1.96)

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