For each of the following situations, state whether a Type I, a Type II, or neit
ID: 3255812 • Letter: F
Question
For each of the following situations, state whether a Type I, a Type II, or neither error has been made. Explain briefly. a) A bank wants to know if the enrollment on their website is above 30% based on a small sample of customers. They test H_0: p = 0.3 vs. H_A: p > 0.3 and reject the null hypothesis. Later they find out that actually 28% of all customers enrolled. b) A student tests 100 students to determine whether other students on her campus prefer Coke or Pepsi and fins no evidence that preference for Coke is not 0.5. Later, a marketing company tests all students on campus and finds no difference. c) A human resource analyst wants to know if the applicants this year score, on average, higher on their placements exam than the 52.5 points the candidates averaged last year. She samples 50 recent tests and finds the average to be points. She fails to reject the null hypothesis that the mean is 52.5 points. At the end of the year, they find that the candidates this year had a mean of 55.3 points. d) A pharmaceutical company tests whether a drug lifts the headache relief rate from the 25% achieved by the placebo. They fail to reject the null hypothesis because the P-value is 0.465. Further testing shows that the drug actually relives headaches in 38% of people.Explanation / Answer
Type 1 Error : Incorrect rejection of a true null hypothesis
Type 2 Error: Retaining a false null hypothesis
(a) H): Null hypothesis: p = 0.3
H0 is rejected.
It is learnt H0 is true.
So, it is an error of rejecting a true null hypothesis.
So, it is a Type 1 error.
(b) H0: Null hypothesis: No diffrence in preference
Finds no evidence that preference is not 0.5.i.e., preference is 0.5.
It is learnt that there is no difference.
So, neither error is committed.
(c) H0: Null hypothesis: mean = 52.5
Fails to reject H0. - i.e., retaining null hypothesis.
It is learnt that mean = 55.3.
So, it is retaining a false null hypothesis.
So, it is a Type 2 Error.
(d) H0: Null hypothesis: drug relieves headaches in 25%.
Fail to reject H0. i/e/. retaining H0.
It is learnt that drug relieves headaches in 38%.
So, it is an error of retaining a false null hypothesis.
So, it is a Type 2 Error.
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