Question:
Some smells are perceived as being more feminine or more masculine. Researchers asked a random sample of 300 American adults to score quantitatively the perceived gender-orientation of lavender. Smaller scores indicate a more feminine scent and larger scores a more masculine scent. In this design, a gender-neutral scent would have a perceived gender-orientation score of 12. The participants gave the scent of lavender an average score of 10.28.
Is this evidence that the scent of lavender is not gender neutral, on average? Select the correct statement of H0, Ha, and the hypotheses parameter in the corresponding test. -
a) Let µ be the mean gender-orientation score for all smells being studied. We test H0: µ=12 versus Ha: µ≠12 ; The alternative is two-sided because we want to test if all of the smells are not gender-neutral.
b) Let µ be the mean gender-orientation score for lavender. We test H0:µ=1.28 versus Ha:µ≠10.28; The alternative is two-sided because we want to test if lavender is not gender-neutral.
c) Let µ be the mean gender-orientation score for lavender. We test H0: µ=12 versus Ha: µ≠12; The alternative is two-sided because we want to test if lavender is not gender-neutral.
d) Let µ be the mean gender-orientation score for lavender. We test H0: µ < 12 versus Ha: ≥ 12 ; The alternative is not two-sided because we want to test if lavender is gender-neutral.
Answer:
c) Let µ be the mean gender-orientation score for lavender. We test H0: µ=12 versus Ha: µ≠12; The alternative is two-sided because we want to test if lavender is not gender-neutral.
Step-by-step explanation:
Here, some smells are perceived to be more feminine while some are more masculine. The researcher picked a sample size of 300 american adults to score quantitatively the perceived gender-orientation of lavender.
We are told that when the score is smaller it indicates a mord feminine scent, when the score is larger it indicates a more masculine scent while a score of 12 indicates a gender neutral scent.
In this case the participants gave lavender a score of 10.28
From the above information we have the following :
Mean, µ = 12
Sample size = 300
Sample mean x' = 10.28
Since the sample mean is less than 12, the null and alternative hypotheses will be:
H0 : µ = 12
Ha : µ ≠ 12
This is a two tailed test because the alternative hypothesis is not gender based, which means lavender could be perceived to be either more feminine or more masculine.
The correct option is option C.
c) Let µ be the mean gender-orientation score for lavender. We test H0: µ=12 versus Ha: µ≠12; The alternative is two-sided because we want to test if lavender is not gender-neutral.
