A researcher is interested in estimating the population mean from a sample of size 20 with a sample mean of 30 and a sample standard deviation of 4. What is the t-value for a 95% confidence level?
Answer
\(\text{Step 6: Look up the t-value for a 95% confidence level and 19 degrees of freedom in the t-distribution table. According to the t-distribution table, the t-value is approximately } 2.093 \)
Step 1 ：\(\text{Step 1: Identify the sample size, which is } n = 20 \)
Step 2 ：\(\text{Step 2: Identify the sample mean, which is } \bar{x} = 30 \)
Step 3 ：\(\text{Step 3: Identify the sample standard deviation, which is } s = 4 \)
Step 4 ：\(\text{Step 4: Identify the confidence level, which is } 95\% \)
Step 5 ：\(\text{Step 5: Determine the degrees of freedom, which is } df = n - 1 = 20 - 1 = 19 \)
Step 6 ：\(\text{Step 6: Look up the t-value for a 95% confidence level and 19 degrees of freedom in the t-distribution table. According to the t-distribution table, the t-value is approximately } 2.093 \)
