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Unformatted text preview: to 0. So yes, the results of the hypothesis test and conﬁdence interval
16. A high school student is considering attending a nearby university. She is concerned that too many of
the students attending the university live at home, and she has decided not to attend if there is strong
evidence that more than 75% of the registered students live at home.
The student experiences a fortunate coincidence. She recently ﬁnished a course in Advanced Placement
Statistics, and the university student newspaper has published a poll of 400 randomly selected students
at the university. 325 of these students reported that they still lived at home.
(a) Write the hypotheses in symbols and in words for testing whether more than 75% of students at
this college live at home.
H0 : p = 0.75 (75% of students at this college live at home)
HA : p > 0.75 (More than 75% of students at this college live at home)
(b) Are the assumptions and conditions for inference satisﬁed?
1. Independence Assumption:
• Random Sampling Condition: We are told that the sample is random.
• 10% Condition: We can safely assume that 400 < 10% of all students at a college.
Since we have a random sample and the 10% condition is satisﬁed, we can assume that whether
or not one student in this sample lives at home is independent of another.
2. Nearly Normal Condition: First we must check if the success failure condition is met.
np ≥ 10 → 400 ∗ 0.75 = 300 > 10
nq ≥ 10 → 400 ∗ 0.25 = 100 > 10 Since the observations are independent and the success-failure condition is met, we can assume
that p is nearly normal.
ˆ 12 (c) Calculate the test statistic.
0.8125 − 0.75
ˆ n 400 (d) Find and interpret the p-value in context.
p-value = P (ˆ > 0.8125|p = 0.75) = P (z > 2.89) = 1 − 0.9981 = 0.0019
If in fact 75% of student at this college lived at home, the probability of getting a random sample
of 400 students where more than 325 live at home would be 0.0019.
(e) Based on the hypothesis test do the data provide convincing evidence to suggest that more than
75% of students at this college live at home? Explain. Use α = 0.025.
Yes, since p-value < 0.025, we reject H0 . The data provide convincing evidence to suggest that
more than 75% of students at this college live at home
(f) What type of error might you have committed?
We may have committed a Type I error since we rejected H0 .
17. A genetic test is used to determine if people have a genetic predisposition for thrombosis, the formation
of a blood clot inside a blood vessel that obstructs the ﬂow of blood through the circulatory system.
It is believed that 3% of the people actually have this predisposition. This test is 99% accurate if
a person actually has the predisposition, meaning that the probability of a positive test result when
a person actually has the predisposition is 0.99. The test is 98% accurate if a person does not have
the predisposition, me...
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This document was uploaded on 12/04/2013.
- Winter '13