The researcher would like to determine if these data provide convincing evidence that the true mean amount of time volunteers who were given training held their breath is greater than the volunteers without training. The researcher 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 greater than 0 , where mu sub 1 is equal to the true mean amount of time that volunteers who were given training held their breath and mu sub 2 is equal to the true mean amount of time that volunteers without training held their breath. The conditions for inference are met. What is the value of the test statistic for a t -test about a difference in means?
Answer
A
t is equal to the fraction with numerator 89 point 6 7 minus 48 point 3 3 and denominator square root of the fraction with numerator 15 point 8 3 squared and denominator 6 plus the fraction with numerator 9 point 8 1 squared and denominator 6 end root
B
t is equal to the fraction with numerator 89 point 6 7 minus 48 point 3 3 and denominator square root of the fraction with numerator 15 point 8 3 squared and denominator 5 plus the fraction with numerator 9 point 8 1 squared and denominator 5 end root
C
t is equal to the fraction with numerator 89 point 6 7 minus 48 point 3 3 and denominator square root of the fraction with numerator 15 point 8 3 times open paren 1 minus 15 point 8 3 close paren and denominator 5 plus the fraction with numerator 9 point 8 1 times open paren 1 minus 9 point 8 1 close paren and denominator 5 end root
D
t is equal to the fraction with numerator 89 point 6 7 minus 48 point 3 3 and denominator square root of the fraction with numerator 15 point 8 3 times open paren 1 minus 15 point 8 3 close paren and denominator 6 plus the fraction with numerator 9 point 8 1 times open paren 1 minus 9 point 8 1 close paren and denominator 6 end root
Explanation
For a two-sample t-test, calculate the difference between the sample means and divide by its standard error: (89.67 − 48.33) / √(15.83²/6 + 9.81²/6). Each group has 6 volunteers, so each sample variance is divided by 6. This is choice A, the formula using the two sample standard deviations and group sizes.
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