For students who first enrolled in two year public institutions in a recent seme
ID: 3268314 • Letter: F
Question
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 0.399. The president of a certain college believes that the proportion of students who enroll in her institution have a higher 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. (a) State the hypotheses H_0: H_1: (Type integers or decimals. Do not round.) (b) Which of the following is a Type I error? A. The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.399, when, in fact, the proportion is greater than 0.399. B. The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.399, when, in fact, the proportion is 0.399. C. The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.399, when, in fact, the proportion is 0.399. D. The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.399, when, in fact, the proportion is greater than 0.399. (c) Which of the following is a Type II error? A. The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.399, when, in fact, the proportion is greater than 0.399. B. The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.399, when, in fact, the proportion is greater than 0.399.Explanation / Answer
(a) H0: Null hypothesis: P = 0.399
HA: Alternative hypothesis: P > 0.399
(b) Type I: Incorrect rejection of a true Null Hypothesis.
Supprein reality P = 0.399. But, due to the testing, we wrongly conclude P > 0.399. Here, Type I Error ia committed.
Thus, correct option:
B. Thepresident rejects the hypothesis that the proportion of students who earn a bachelor's degreewithin six years is 0.399 when in fact the proportion is 0.399
(c) Type II Error:
Incorrectly retaining a false null hypothesis.
Suppose in reality P > 0.399. But, due to testing, we concluse P = 0.399. Type II Error is committed.
So, Correct option:
B. The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.399 when in fact the proportion is greater than 0.399.