A researcher wishes to determine if students are able to complete a certain puzzle more quickly while exposed to a pleasant floral scent. Suppose the time (in seconds) needed for high school students to complete the puzzle while exposed to the scent follows a normal distribution with mean $\mu$ and standard deviation $\sigma$ = 4. Suppose also, that in the general population of all high school students, the time needed to complete the puzzle follows a normal distribution with mean 80 and standard deviation $\sigma$ = 4. The researcher, therefore, decides to test the hypotheses: H₀: $\mu$ = 80 H_a: $\mu$

Question

A researcher wishes to determine if students are able to complete a certain puzzle more quickly while exposed to a pleasant floral scent. Suppose the time (in seconds) needed for high school students to complete the puzzle while exposed to the scent follows a normal distribution with mean $\mu$ and standard deviation $\sigma$ = 4. Suppose also, that in the general population of all high school students, the time needed to complete the puzzle follows a normal distribution with mean 80 and standard deviation $\sigma$ = 4. The researcher, therefore, decides to test the hypotheses: H₀: $\mu$ = 80 H_a: $\mu$ < 80 To do so, the researcher has 10,000 high school students complete the puzzle in the presence of the floral scent. The mean time for these students is = 79.8 seconds and the P-value is less than 0.0001. It is appropriate to conclude which of the following? A) The researcher has proved that, for high school students, a pleasant floral scent substantially improves the time it takes to complete the puzzle. B) The researcher has strong evidence that, for high school students, a pleasant floral scent improves the time it takes to complete the puzzle. C) The researcher has moderate evidence that, for high school students, a pleasant floral scent substantially improves the time it takes to complete the puzzle. D) None of the the answer choices are correct. With such a large sample size, statistically significant results may not be of any practical importance.

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The Answer of A researcher wishes to determine if students are able to complete a certain puzzle more quickly while exposed to a pleasant floral scent. Suppose the time (in seconds) needed for high school students to complete the puzzle while exposed to the scent follows a normal distribution with mean $\mu$ and standard deviation $\sigma$ = 4. Suppose also, that in the general population of all high school students, the time needed to complete the puzzle follows a normal distribution with mean 80 and standard deviation $\sigma$ = 4. The researcher, therefore, decides to test the hypotheses: H₀: $\mu$ = 80 H_a: $\mu$ < 80 To do so, the researcher has 10,000 high school students complete the puzzle in the presence of the floral scent. The mean time for these students is = 79.8 seconds and the P-value is less than 0.0001. It is appropriate to conclude which of the following? A) The researcher has proved that, for high school students, a pleasant floral scent substantially improves the time it takes to complete the puzzle. B) The researcher has strong evidence that, for high school students, a pleasant floral scent improves the time it takes to complete the puzzle. C) The researcher has moderate evidence that, for high school students, a pleasant floral scent substantially improves the time it takes to complete the puzzle. D) None of the the answer choices are correct. With such a large sample size, statistically significant results may not be of any practical importance.

A Researcher Wishes to Determine If Students Are Able to Complete