Question

A simple random sample of 100 flights of a large airline (call this airline 1) showed that 64 were on time. A simple random sample of 100 flights of another large airline (call this airline 2) showed that 80 were on time. Let p1 and p2 be the proportion of all flights that are on time for these two airlines.

If the 90% confidence interval for the difference p1 – p2 is –0.157 ± 0.102. Is there evidence of a difference in the on-time rate for the two airlines? To determine this, test the hypotheses H0: p1 = p2 versus Ha: p1p2. Based on the 90% confidence interval, answer each of the following questions with yes, no, or can’t tell.

A)

Is the

P

-value less than 0.001?

B)

Is it true that 0.05 <

P

-value < 0.10?

C)

Is the

P

-value less than 0.10?

D)

Is the

P

-value greater than 0.10?

Answer 1

For 90% confidence interval:

Lower limit = -0.157 - 0.102 = -0.259

Upper limit = -0.157 + 0.102 = -0.055

As the confidence interval does not contain 0 and both the values negative we can reject the null hypothesis.

That means the p-value is less than 0.10.

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A) Is the P -value less than 0.001?

Answer: Can't tell.

B) Is it true that 0.05 < P -value < 0.10?

Answer: Can't tell.

C) Is the P -value less than 0.10?

Answer: yes

D) Is the P -value greater than 0.10?

Answer: No.