Question

Morgan wants to test the speed for two different routes she can take to ride her bicycle home from work. Route A involves riding her bicycle on a busy road, and Route B involves riding her bicycle along a scenic trail.

Morgan collects some initial data, given in the table below:

Route A	Route B
?⎯⎯⎯=10 minutes	?⎯⎯⎯=7 minutes
?=4 minutes	?=5 minutes
?=7	?=6

Based on Morgan's initial data, she conducts a hypothesis test to determine whether there is a statistically significant difference between the two routes, and finds a p-value of 0.1330 for the hypotheses:

?0:??−??≤0

??:??−??>0

Choose the answer below that best interprets this result.Select your answer from one of the following options.

• a.The sample does not provide enough evidence to refute the claim that Route B is faster.
• b.This sample does not provide enough evidence to support the claim that Route B is faster. Even though the difference is large (3 minutes), the small sample size means that this difference could be due to random chance.
• c.This sample provides evidence that Route A and Route B are approximately the same, because we were not able to conclude that Route B is faster.
• d.This sample provides enough evidence to support the claim that Route B is faster, because the sample average time to complete route B is smaller.

Morgan discovers a third route, Route C, which consists of small country roads. She decides to collect more data about Route B and C, and finds the following:

Route C	Route B
?⎯⎯⎯=8 minutes	?⎯⎯⎯=7 minutes
?=2.1 minutes	?=2.4 minutes
?=100	?=100

She conducts another hypothesis test, and finds a p-value of 0.0010 for the hypotheses:

?0:??−??≤0

??:??−??>0

Choose the answer below that best interprets this result.Select your answer from one of the following options.

• a.This sample does not provide evidence that Route B is faster than Route C, because the difference between them is only 1 minute.
• b.This sample does not provide evidence that Route B is faster than Route C, because the p-value is not significant.
• c.This sample provides evidence that Route B is faster than Route C. Since the p-value is much smaller than 0.05, Route B is much faster than Route C.
• d.This sample provides evidence that Route B is faster than Route C. Even though the difference is small (1 minute), the large sample size provides a lot of evidence that the difference is statistically significant.

The two data sets given in this problem show that:Select your answer from one of the following options.

• a.Large samples can show a practical difference without being statistically significant, while small samples may show a statistically significant difference that has little/no practical application.
• b.Small samples can show a practical difference without being statistically significant, while large samples may show a statistically significant difference that has little/no practical application.
• c.The larger the p-value, the bigger the difference between two averages.
• d.The smaller the p-value, the bigger the difference between two averages.

Answer 1