BlueSky Air claims that at least 80% of its flights arrive on time. A random sample of 160 BlueSky Air flights revealed that 115 arrive on time. Do the data provide sufficient evidence to contradict the claim by BlueSky Air?

Part i) What is the parameter of interest?

A. All BlueSky Air flights.
B. Whether a BlueSky Air flight arrives on time.
C. The proportion of the 160 BlueSky Air flights that arrive on time.
D. The proportion of all BlueSky Air flights that arrive on time.

Part ii) Let $p$ be the population proportion of flights that arrive on time. What are the null and alternative hypotheses?

A. Null: $p = 0.80$. Alternative: $p < 0.80$.
B. Null: $p = 0.80$. Alternative: $p > 0.80$.
C. Null: $p = 115/160$. Alternative: $p \ne 115/160$.
D. Null: $p < 0.80$. Alternative: $p \ge 0.80$.
E. Null: $p = 0.80$. Alternative: $p \ne 0.80$.
F. Null: $p > 0.80$. Alternative: $p \le 0.80$.

Part iii) The $P$-value is computed to be 0.0051. Using all of the information available to you, which of the following is/are correct? (check all that apply)

A. The observed proportion of flights that arrive on time is unusually high if BlueSky Air's claim is true.
B. The observed proportion of flights that arrive on time is unusually low if BlueSky Air's claim is false.
C. Assuming BlueSky's claim is false, there is a 0.0051 probability that in a random sample of 160 flights, 115 or fewer flights arrive on time.
D. The observed proportion of flights that arrive on time is unusually high if BlueSky Air's claim is false.
E. The observed proportion of flights that arrive on time is unusually low if BlueSky Air's claim is true.
F. There is a 0.0051 probability that BlueSky Air's claim is true.
G. Assuming BlueSky's claim is true, there is a 0.0051 probability that in a random sample of 160 flights, 115 or fewer flights arrive on time.

Part iv) Based on the $P$-value (0.0051) obtained, at the 1% significance level, ...

A. we should not reject the null hypothesis.
B. we should reject the null hypothesis.

Part v) What is an appropriate conclusion for the hypothesis test at the 1% significance level?

A. There is sufficient evidence to support BlueSky Air's claim.
B. BlueSky Air's claim is false.
C. BlueSky Air's claim is true.
D. There is sufficient evidence to contradict BlueSky Air's claim.

Part vi) Which of the following scenarios describe the Type I error of the test?

A. The data suggest that BlueSky Air's claim is true when in fact the claim is false.
B. The data suggest that BlueSky Air's claim is false when in fact the claim is false.
C. The data suggest that BlueSky Air's claim is true when in fact the claim is true.
D. The data suggest that BlueSky Air's claim is false when in fact the claim is true.

Part vii) Based on the result of the hypothesis test, which of the following types of errors are we in a position of committing?

A. Both Type I and Type II errors.
B. Type I error only.
C. Type II error only.
D. Neither Type I nor Type II errors.