In the 1980's the average age at which Australian men first married was 24.3 years. It is widely suspected that young people today are waiting longer to get married. The manager of a formal wear hire business records the ages of 15 first-time grooms.

22 20 24 31 28

27 24 38 31 32

Can we conclude, at a 5% significance level, that the true mean age of first-time grooms is greater than 24.3 years?