For students who first enrolled in two year public institutions in a recent semester, the proportion who earned a bachelor's degree within six years was 0.396. The president of a certain college believes that the proportion of students who enroll in her institution have a lower completion rate. (a) Determine the null and alternative hypotheses. (b) Explain what it would mean to make a Type I error. (c) Explain what it would mean to make a Type II error.

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For students who first enrolled in two year public institutions in a recent semester, the proportion who earned a bachelor's degree within six years was 0.396. The president of a certain college believes that the proportion of
students who enroll in her institution have a lower completion rate.
(a) Determine the null and alternative hypotheses.
(b) Explain what it would mean to make a Type I error.
(c) Explain what it would mean to make a Type Il error.
(a) State the hypotheses.
Ho:
H₁:
(Type integers or decimals. Do not round.)
(b) Which of the following is a Type I error?
A. The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.396, when, in fact, the proportion is 0.396.
B. The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.396, when, in fact, the proportion is less than 0.396.
C. The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.396, when, in fact, the proportion is 0.396.
D. The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.396, when, in fact, the proportion is less than 0.396.
(c) Which of the following is a Type II error?
A. The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.396, when, in fact, the proportion is less than 0.396.
B. The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.396, when, in fact, the proportion is 0.396.
C. The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.396, when, in fact, the proportion is less than 0.396.
D. The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.396, when, in fact, the proportion is 0.396.
Transcribed Image Text:For students who first enrolled in two year public institutions in a recent semester, the proportion who earned a bachelor's degree within six years was 0.396. The president of a certain college believes that the proportion of students who enroll in her institution have a lower completion rate. (a) Determine the null and alternative hypotheses. (b) Explain what it would mean to make a Type I error. (c) Explain what it would mean to make a Type Il error. (a) State the hypotheses. Ho: H₁: (Type integers or decimals. Do not round.) (b) Which of the following is a Type I error? A. The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.396, when, in fact, the proportion is 0.396. B. The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.396, when, in fact, the proportion is less than 0.396. C. The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.396, when, in fact, the proportion is 0.396. D. The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.396, when, in fact, the proportion is less than 0.396. (c) Which of the following is a Type II error? A. The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.396, when, in fact, the proportion is less than 0.396. B. The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.396, when, in fact, the proportion is 0.396. C. The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.396, when, in fact, the proportion is less than 0.396. D. The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.396, when, in fact, the proportion is 0.396.
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