A nurse at a local hospital wonders if the firstborn twin is taller than the second-born. He randomly selects the medical records of 33 sets of twins and finds the differences open paren firstborn minus second-born close paren in the twins’ heights, in centimeters. The mean of the differences is 1 point 1 centimeters with a standard deviation of 2 point 3 centimeters. Assuming that the conditions for inference are met, what is the test statistic for testing the hypotheses ratio of cap h sub 0 to mu sub diff is equal to 0 , ratio of cap h sub A to mu sub diff is greater than 0 ?
Answer
A
t is equal to the fraction with numerator 1 point 1 minus 0 and denominator the fraction with numerator 2 point 3 and denominator square root of 33
B
t is equal to the fraction with numerator 0 minus 1 point 1 and denominator the fraction with numerator 2 point 3 and denominator square root of 33
C
t is equal to the fraction with numerator 0 minus 1 point 1 and denominator the fraction with numerator 2 point 3 and denominator square root of 33
D
t is equal to the fraction with numerator 1 point 1 minus 0 and denominator square root of 2 point 3 over 33 end root
Explanation
For a one-sample t-test, the test statistic is (sample mean − hypothesized mean) ÷ (sample standard deviation ÷ √sample size). Substituting the values gives t = (1.1 − 0) ÷ (2.3 ÷ √33), which is about 2.74. This matches choice A, the formula with 1.1 − 0 in the numerator and 2.3/√33 in the denominator.
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