A statistical question

Problem: Analysis of user purchasing behavior on e-commerce platforms

Background: An e-commerce platform wants to study whether the average purchase amount of users is affected by membership level (ordinary members vs. gold members). The most recent order amount (in US dollars) of 30 ordinary members and 30 gold members was randomly selected, and the data is as follows:

Ordinary members: sample mean = $85, sample standard deviation = $15

Gold members: sample mean = $110, sample standard deviation = $20

Task:

1. Descriptive statistics: Calculate the 95% confidence interval of the two sets of data and explain the results.

2. Hypothesis test: At the significance level α=0.05, test whether there is a significant difference in the average purchase amount of the two types of members.

Propose the null hypothesis (H₀) and the alternative hypothesis (H₁).

Choose an appropriate test method (such as independent sample t-test) and explain the reason.

Calculate the test statistic and draw a conclusion.

3. Additional thinking: If the p-value in the actual analysis is 0.03, but the platform manager explains that “the difference may be caused by sampling error”, how to respond?