Respuesta :
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).
The correct interpretation is, 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.
Given that,
A magazine article reported that college students spend an average of $100 on a first date.
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.
We have to determine,
Which of the following is a correct interpretation of the P-value.
According to the question,
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.
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.
Hence, The correct interpretation is, 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.
For more information about Probability click the link given below.
https://brainly.com/question/16292432
