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=0.3vs.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 recent tests and finds the average to be 54.1 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 head ache 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 of people.

Answer 1

Type I

No error

Type II

Type II

Explanation:

Type I error: A type I error occurs when the null hypothesis is rejected when it is actually true

Type II error: A type II error occurs when the one fails to reject the null hypothesis when it is actually not true.

Type I Type II

Reject H₀ when true Accept H₀ when not true

a. A type I error has been made since we rejected the null hypothesis when it was actually true. Proportion was actually 28%.

b. Neither error has been made because there is no evidence of an alternative hypothesis been made.

c. A type II error has been made because she failed to reject the null when it was actually not true i e the mean is different and higher than the null hypothesis.

d. A type II error was made since we fail to reject the null hypothesis when the value observed was actually higher than 25%.