A recent survey of 8 comma 000 high school students found that the mean price of a prom dress was 195 point 0 0 dollars with a standard deviation of 12 point 0 0 dollars Alyssa thinks that her school is more fashion conscious and that students spent more than $195.00 She collected data from 20 people in her high school and found that the average price spent on a prom dress was 208 point 0 0 dollars Which of the following are the correct null hypothesis and alternate hypothesis?
Answer
A
ratio of cap h sub 0 to mu is equal to 195 ; ratio of cap h sub A to mu is greater than 195
B
ratio of cap h sub 0 to mu is less than 195 ; ratio of cap h sub A to mu is greater than or equal to 208
C
ratio of cap h sub 0 to mu is equal to 195 ; ratio of cap h sub A to mu is not equal to 195
D
ratio of cap h sub 0 to mu is not equal to 195 ; ratio of cap h sub A to mu is equal to 208
Explanation
Alyssa is testing whether the average prom-dress price at her school is greater than the reported average of $195. The null hypothesis uses equality, so H₀: μ = 195, and the one-sided alternative is Hₐ: μ > 195. The sample average of $208 is evidence to evaluate the claim; it does not replace the population mean in the hypotheses. Choice A states the correct hypotheses.
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