6
QuizMultiple Choice

Testing a Claim about a Difference between Means

Question 6 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)

Timmy could follow two main routes to get to school. Timmy believes that route 1 is faster than route 2. To investigate, he decides to keep track for the next 4 weeks. Each morning, he flips a coin to determine which route he takes. Of the 20 school days, 12 days were randomly assigned to route 1, and 8 days were randomly assigned to route 2. The mean travel time for days assigned to route 1 was 20 minutes with a standard deviation of 3 minutes. The mean travel time for the days assigned to route 2 was 22 minutes with a standard deviation of 2 minutes. Timmy would like to know if the data provide convincing evidence of a difference in travel time for the 2 routes. Let μ1 = the true mean travel time to school along route 1 and μ2 = the true mean travel time to school along route 2. Dotplots of the distribution of travel time for route 1 and route 2 show no strong skewness or outliers. Are the conditions for inference met?

Answer
A
No, the random condition is not met.
B
No, the 10% condition is not met.
C
No, the Normal/large sample condition is not met.
D
Yes, all of the conditions for inference have been met.
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