Example 7.8. From a random sample of n 100 Xavier students, 75 are in relationsh
ID: 3364291 • Letter: E
Question
Example 7.8. From a random sample of n 100 Xavier students, 75 are in relationships We wish to test if the proportion of all Xavier students who are in relationships is greater than 0.60. Use a significance level of = 0.05. (a) What is the null and alternative hypotheses? (b) Suppose our test produces a p-value of 0.0011 and thus you reject the null hypothesis in favor of the alternative hypothesis. If we made an error, which type of error did we make? Type 1 or type 2? at() (c) In the proper context, interpret making the type of error you chose in t (d) Name a potential consequence of making this type of error. Feel free to get creative!Explanation / Answer
(a) We have to test, H0: p = 0.60 against p > 0.60,
where p denotes the proportion of Xavier students, who are in
a relationship. H0 and H1 are the null and alternative
hypotheses respectively.
(b) Since, we have rejected H0, when it is actually true, we
have made Type-I error.
(c) Here, we have rejected the null hypothesis, when it should
not have been rejected, i.e. there is not sufficient evidence to
reject H0. We concluded that that the proportion of Xavier
students who are in a relationship is significantly more than
0.60, when actually it is not. It resulted in increasing the
number of False positives.
(d) Type-I error is more fatal than Type-II error. So, we have
ended up concluding that proportion of students who are in a
relationship is significant greater than 0.60. It suggests we
have taken some relationships into consideration which
doesn't even exist!
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