6
QuizMultiple Choice

Testing a Claim about a Difference between Means — Quiz

Question 6 • Statistics

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, so he tests ratio of cap h sub 0 to mu sub 1 minus mu sub 2 is equal to 0 , ratio of cap h sub A to mu sub 1 minus mu sub 2 is not equal to 0 Let mu sub 1 is equal to the true mean travel time to school along route 1 and mu sub 2 is equal to 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. The conditions for inference have been met. What are the values of the test statistic and cap p -value for a t - test about a difference in means? Use the t -table.

Answer
A
t is equal to negative 1 point 7 9 . The cap p -value is between 0 point 0 2 5 and 0 point 0 5 .
B
t is equal to negative 1 point 7 9 . The cap p -value is between 0 point 0 5 and 0 point 1 0 .
C
t is equal to 1 point 7 9 . The cap p -value is between 0 point 0 2 5 and 0 point 0 5 .
D
t is equal to 1 point 7 9 . The cap p -value is between 0 point 0 5 and 0 point 1 0 .

Explanation

The difference in sample means is 20 − 22 = −2 minutes. Its standard error is √(3²/12 + 2²/8) = √1.25 ≈ 1.118, so the test statistic is t = −2/1.118 ≈ −1.79. Using about 18 degrees of freedom, a two-sided t-table comparison places the P-value between 0.05 and 0.10. Thus, choice B gives the test statistic and P-value range.

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