Describe a scenario where you would use a t-test instead of a z-test?

In my statistics class, I conducted a project analyzing the exam scores of 15 students who took a new study program. Since my sample size was small and I didn't have access to the population standard deviation, I decided to use a t-test to determine if the new study program significantly improved scores compared to previous exams. After gathering the data, I calculated the mean scores and applied the t-test, which revealed a statistically significant improvement. This experience helped me understand the importance of choosing the right statistical test based on sample size and available data.

While volunteering for a local community center, I helped assess the impact of a three-week training program on participants' confidence levels. We surveyed 20 individuals before and after the training, and since we were working with a small group without a known population variance, a t-test was the logical choice. By comparing the pre- and post-training confidence scores, we found a meaningful increase, which I presented in our final report. This experience taught me how to apply statistical methods in real-life situations and reinforced the importance of understanding when to use a t-test.

In my first job as a data analyst for a startup, I was tasked with analyzing customer feedback from a survey of 50 respondents. Although the sample was slightly larger, we still did not know the population variance because we were a new company. I opted for a t-test to compare the satisfaction rating before and after implementing some changes to our service. The analysis revealed that customer satisfaction had significantly increased, guiding our future strategies. This experience highlighted how important it is to select the right statistical test based on the context of the data.