For each of the following situations, state whether a Type I, a Type II, or neit
ID: 3182652 • 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 H0:p=0.3 vs Ha: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 finds 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 placement exam than the 52.5 points the candidates averaged last year. She samples 50 recenet tests and finds the average to be 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 placebeo. 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
In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis (a "false positive"), while a type II error is incorrectly retaining a false null hypothesis (a "false negative").
a) Here Type I error is made as rejecting H0 means accepting H1 which states 30% enrolled but actually only 28% enrolled.
b) Here Type I error is made as actually there was no difference in preference but it was wrongly accepted that difference is there.
c) Here Type II error is made as H0: mean=52.5 vs H1:mu>52.5. Human resource analyst found that mean was 52.5 but later it was found that mean was 55.3.
d)Here Type II error is made as they accepted the wrong null hypothesis, they found that relief rate was 25% but actually it was 38%
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