Question

A magazine article reported that college students spend an average of $100 on a first date. A university sociologist believed that number was too high for the students at the university. The sociologist surveyed 32 randomly selected students from the university and obtained a sample mean of $92.23 for the most recent first dates. A one-sample t-test resulted in a P-value of 0.026. Which of the following is a correct interpretation of the P-value?
a) The probability is 0.026 that the mean amount of money students from the university spend on a first date is less than $100.
b) The probability is 0.026 that the mean amount of money students from the university spend on a first date is less than $92.23.
c) The probability is 0.026 that the mean amount of money students from the university spend on a first date is more than $92.23.
d) If the mean amount of money that students from the university spend on a first date is $100, the probability is 0.026 that a randomly selected group of 32 students from the university would spend a mean of $92.23 or less on their most recent first dates.
e) If the mean amount of money that students from the university spend on a first date is less than $100, the probability is 0.026 that a randomly selected group of 32 students from the university would spend a mean of $92.23 or less on their most recent first dates.

Answer 1

Answer:

The correct option is (d).

Step-by-step explanation:

The p-value is well defined as the probability, [under the null hypothesis (H₀)], 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 p-value of a statistic is lower than the level of significance α.

A small p-value (typically ≤ 0.05) specifies solid proof against the null hypothesis (H₀), so you discard H₀.

A large p-value (> 0.05) specifies fragile proof against the H₀, so you fail to discard H₀.

The hypothesis in this case can be defined as follows:

H₀: The mean amount of money students from the university spend on a first date is $100, i.e. μ = 100.

Hₐ: The mean amount of money students from the university spend on a first date is less than $100, i.e. μ < 100.

The sample selected is of size, n = 32.

The sample mean amount spent is, $92.23.

The p-value of the test is, p-value = 0.026.

The p-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).