A random sample of costs for 10 different stylists was taken at Hair by Charles and Curl Up & Dye. Do the salons differ in mean costs?

A random sample of costs for 10 different stylists was taken at Hair by Charles and Curl Up & Dye. Do the salons differ in mean costs?

• A. 1-sample t-test
• B. 2-sample t-test
• C. Paired t-test
• D. Chi-square test

Answer: (B)

The main idea is comparing the average cost between two separate groups. Since the costs come from two different salons, the observations in one group are independent of the observations in the other. When you want to know if two independent groups have different means for a continuous variable, the two-sample t-test is the appropriate method. It compares the means while accounting for variability in each group. A one-sample t-test would only compare a single group to a fixed standard value, not to another group's mean. A paired t-test is for related or matched observations (same subjects measured in two conditions or matched pairs), which isn’t the case here. The chi-square test is for categorical data, not for comparing means of a numerical cost variable. So, using the two-sample t-test best answers the question about whether the salons differ in mean costs.

The main idea is comparing the average cost between two separate groups. Since the costs come from two different salons, the observations in one group are independent of the observations in the other. When you want to know if two independent groups have different means for a continuous variable, the two-sample t-test is the appropriate method. It compares the means while accounting for variability in each group. A one-sample t-test would only compare a single group to a fixed standard value, not to another group's mean. A paired t-test is for related or matched observations (same subjects measured in two conditions or matched pairs), which isn’t the case here. The chi-square test is for categorical data, not for comparing means of a numerical cost variable. So, using the two-sample t-test best answers the question about whether the salons differ in mean costs.