A researcher collated data on Americans’ leisure time activities. She found the mean number of hours spent watching television each weekday to be 2 point 7 hours with a standard deviation of 0 point 2 hours. Jonathan believes that his football team buddies watch less television than the average American. He gathered data from 40 football teammates and found the mean to be 2 point 3 Which of the following are the correct null and alternate hypotheses?
Answer
A
ratio of cap h sub 0 to mu is not equal to 2 point 7 ; ratio of cap h sub A to mu is equal to 2 point 3
B
ratio of cap h sub 0 to mu is equal to 2 point 7 ; ratio of cap h sub A to mu is not equal to 2 point 7
C
ratio of cap h sub 0 to mu is less than 2 point 7 ; ratio of cap h sub A to mu is greater than or equal to 2 point 3
D
ratio of cap h sub 0 to mu is greater than or equal to 2 point 7 ; ratio of cap h sub A to mu is less than 2 point 7
Explanation
The researcher’s average for Americans is 2.7 hours per weekday. Since Jonathan believes his teammates watch less, the alternative hypothesis is that their population mean is less than 2.7 hours: Hₐ: μ < 2.7. The null hypothesis includes equality and values not supporting that claim, so H₀: μ ≥ 2.7. This matches choice D.
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