An owner of a construction company wants to know if work times for room additions can be completed faster than the contract times. Which test is appropriate to analyze the evidence?

An owner of a construction company wants to know if work times for room additions can be completed faster than the contract times. Which test is appropriate to analyze the evidence?

• A. 1-sample t-test
• B. 2-sample t-test
• C. 1-proportion z-test
• D. Matched pairs t-test

Answer: (D)

When you have paired measurements from the same projects, you compare the differences within each pair. Here, each room addition has both a contract time and an actual time, so you form the difference for every project (for example, contract time minus actual time). The goal is to see if, on average, the actual times are shorter than the contract times. A matched pairs (paired) t-test is designed exactly for this: it tests whether the mean of those differences differs from zero. If the average difference is positive (meaning actual time is less than contract time), and this difference is statistically significant, you have evidence that work times can be completed faster. This approach is preferred over a two-sample t-test because the two measurements for each project are related; treating them as independent samples would ignore the pairing and could lead to incorrect conclusions. The 1-sample t-test compares a single set of observations to a fixed value, which doesn’t leverage the paired structure here, and the 1-proportion z-test is meant for binary outcomes, not continuous time measurements.

When you have paired measurements from the same projects, you compare the differences within each pair. Here, each room addition has both a contract time and an actual time, so you form the difference for every project (for example, contract time minus actual time). The goal is to see if, on average, the actual times are shorter than the contract times. A matched pairs (paired) t-test is designed exactly for this: it tests whether the mean of those differences differs from zero. If the average difference is positive (meaning actual time is less than contract time), and this difference is statistically significant, you have evidence that work times can be completed faster.

This approach is preferred over a two-sample t-test because the two measurements for each project are related; treating them as independent samples would ignore the pairing and could lead to incorrect conclusions. The 1-sample t-test compares a single set of observations to a fixed value, which doesn’t leverage the paired structure here, and the 1-proportion z-test is meant for binary outcomes, not continuous time measurements.