LECTURE PREP 02: TYPE I & TYPE II ERRORS QUESTIONS & ANSWERS(RATED A+)

LECTURE PREP 02: TYPE I & TYPE II
ERRORS QUESTIONS &
ANSWERS(RATED A+)

Is the following statement true or false? If false, explain briefly. The alpha level
depends on the sample size.

A) The statement is false because the alpha level is set independently and does not
depend on the sample size.
B) The statement is false because the alpha level depends on the p-value, not the
sample size.
C) The statement is false because the alpha level depends on the test statistic, not
the sample size.
D) The statement is true. - ANSWERA) The statement is false because the alpha
level is set independently and does not depend on the sample size.

Is the following statement true or false? If false, explain briefly. If we use an alpha
level of 0.01, a p-value of 0.001 is statistically significant.

A) True.
B) False. If we use an alpha level of 0.01, then a z-score of 0.001 is significant.
C) False. An alpha level of 0.01 gives n significance to a p-value of 0.001.
D) False. A p-value of 0.001 would not be significant since it is less than alpha. -
ANSWERA) True.

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 relieves headaches in
38% of people. Has a Type I error or Type II error been made? Or no error?

A) The company made a Type I error. It used a P-value to determine its conclusion
instead of a critical value.
B) The company made a Type I error. The null hypothesis was not rejected, but it
was false. The true relief rate was greater than 0.25.
C) The company made a Type II error. The null hypothesis was not rejected, but it
was false. The true relief rate was greater than 0.25.
D) The company did not make an error. They did not reject the null hypothesis when
the P-value was almost 0.5.
E) The company made a Type II error. It used a P-value to determine its conclusion
instead of a cri - ANSWERC) The company made a Type II error. The null
hypothesis was not rejected, but it was false. The true relief rate was greater than
0.25.

, A bank wants to know if the enrollment on their website is above 30% based on a
small sample of customers. They test Ho: p = 0.3 vs. Ha: p > 0.3 and reject the null
hypothesis. Later they find out that actually 28% of all customers enrolled. Has a
Type I error or Type II error been made? Or no error?

A) The bank made a Type II error. The actual value is not greater than 0.3 but they
rejected the null hypothesis.
B) The bank made a Type I error. The actual value is not greater than 0.3 but they
rejected the null hypothesis.
C) The bank did not make an error. The actual value is not equal to 0.3 and they
rejected the null hypothesis.
D) The bank made a Type II error. The actual value is close to 0.3 but they rejected
the null hypothesis.
E) The bank made a Type I error. The actual value is close to 0.3 but they rejected
the null hypothesis. - ANSWERB) The bank made a Type I error. The actual value is
not greater than 0.3 but they rejected the null hypothesis.

A student tests 100 students to determine whether other students on her campus
prefer soda brand A or soda brand B and finds no evidence that preference for brand
A is not 0.5. Later, a marketing company tests all students on campus and finds no
difference. Has a Type I error or Type II error been made? Or no error?

A) The student made a Type II error. She found no evidence that preference for
brand A is not a certain value, but the marketing company found no evidence that
preference for brand A is a certain value.
B) The student made a Type II error. She did not reject the null hypothesis.
C) The student made a Type I error. She found no evidence that preference for
brand A is not a certain value, but the marketing company found no evidence that
preference for brand A is a certain value.
D) The student made a Type I error. She did not reject the null hypothesis.
E) The student did not make an error. The actual v - ANSWERE) The student did not
make an error. The actual value is 0.50, which was not rejected.

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. Has a
Type I error or Type II error been made? Or no error?

A) The analyst made a Type I error. The actual value was 55.3 points, which is close
to 52.5.
B) The analyst made a Type II error. The actual value was 55.3 points, which is
greater than 52.5.
C) The analyst did not make an error. The actual value was 55.3 points, which is
close to 52.5.
D) The analyst made a Type II error. The actual value was 55.3 points, which is
close to 52.5.