At a certain university, 22% of students fail general chemistry on their first attempt. Professor Brown teaches at this university and believes that the rate of first-time failure in his general chemistry classes is 45%. He samples 86 students from last semester who were first-time enrollees in general chemistry and finds that 19 of them failed his course.
i). State the appropriate null and alternate hypotheses.
ii). Compute the test statistic z.
iii). Using $\alpha = 0.05$ can you conclude that the percentage of failures differs from 45%?

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The Answer of At a certain university, 22% of students fail general chemistry on their first attempt. Professor Brown teaches at this university and believes that the rate of first-time failure in his general chemistry classes is 45%. He samples 86 students from last semester who were first-time enrollees in general chemistry and finds that 19 of them failed his course.
i). State the appropriate null and alternate hypotheses.
ii). Compute the test statistic z.
iii). Using $\alpha = 0.05$ can you conclude that the percentage of failures differs from 45%?

At a Certain University, 22% of Students Fail General Chemistry α=0.05\alpha = 0.05α=0.05

At a Certain University, 22% of Students Fail General Chemistry $\alpha = 0.05$