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

The correct answer is (D)

Step-by-step explanation:

Solution

For the value p, the correct interpretation is: Under null hypothesis the probability of obtaining the sample observations

From the question given,the right answer 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

Answer 2

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

Step-by-step explanation:

Given that:

mean amount of money spent by the students is= $100

Surveyed of random selection of 32 students is obtained from the university

sample result a mean value of $92.23

The p-value = 0.026

The p-value is the probability value that helps to determinethe observed or more extreme results when the null hypothesis H₀ of a study question is true.

From the question; the correct interpretation of the p-value 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