Answer:
The correct option is (d).
Step-by-step explanation:
The <em>p</em>-value is well defined as the probability, [under the null hypothesis (<em>H₀</em>)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic.
We reject a hypothesis if the <em>p</em>-value of a statistic is lower than the level of significance <em>α</em>.
A small <em>p</em>-value (typically ≤ 0.05) specifies solid proof against the null hypothesis (<em>H₀</em>), so you discard <em>H₀</em>.
A large <em>p</em>-value (> 0.05) specifies fragile proof against the <em>H₀</em>, so you fail to discard <em>H₀</em>.
The hypothesis in this case can be defined as follows:
<em>H₀</em>: The mean amount of money students from the university spend on a first date is $100, i.e. <em>μ</em> = 100.
<em>Hₐ</em>: The mean amount of money students from the university spend on a first date is less than $100, i.e. <em>μ</em> < 100.
The sample selected is of size, <em>n</em> = 32.
The sample mean amount spent is, $92.23.
The <em>p</em>-value of the test is, <em>p</em>-value = 0.026.
The <em>p</em>-value in this case can be defined as the probability that the sample mean amount spent on first date by the 32 students is less than or equal to $92.23, given that the actual mean amount spent on first date is $100.
Thus, the correct option is (d).