A magazine article reported that college students spend an average of $100 on a first date. A university sociologist believed th

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2 months ago

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A magazine article reported that college students spend an average of $100 on a first date. A university sociologist believed th

at 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.

Mathematics

1 answer:

Inessa [12.5K] · Answer 1 · 2026-02-18T15:11:57+03:00

Answer:

The correct answer is (d).

Step-by-step explanation:

The p-value provides the probability, given the null hypothesis (H₀), of obtaining a result at least as extreme as the observed test statistic.

A hypothesis is rejected if the p-value is less than the significance level α.

A low p-value (often ≤ 0.05) presents strong evidence against the null hypothesis (H₀), leading to its rejection.

A high p-value (> 0.05) indicates weak evidence against H₀, resulting in failure to reject H₀.

The hypothesis in this scenario is formulated as follows:

H₀: The average expenditure by university students on a first date is $100, or μ = 100.

Hₐ: The average expenditure by university students on a first date is under $100, or μ < 100.

The sample consists of n = 32.

The mean expenditure recorded is $92.23.

The calculated p-value stands at p-value = 0.026.

This p-value signifies the probability that the mean expenditure on a first date by the sampled 32 students is less than or equal to $92.23, assuming the true mean expenditure is $100.