To determine the value of t for a 95% confidence interval with 10 pieces of data, we first need to consider the concept of confidence intervals and how the t-distribution applies in this scenario.
When calculating confidence intervals, the t-distribution is used instead of the normal distribution when the sample size is small (typically n < 30) and the population standard deviation is unknown. Since we have 10 data points, we will indeed be using the t-distribution.
To find the appropriate t-value, follow these steps:
- Identify the degrees of freedom: For a single sample, the degrees of freedom (df) are calculated as the sample size minus one. So, in this case:
- df = n – 1 = 10 – 1 = 9
- Consult a t-distribution table: Look up the critical t-value in a t-table using the degrees of freedom and the desired confidence level. For a 95% confidence interval, we need the critical value for 0.025 in the right tail since this leaves 2.5% in each tail (100% – 95% = 5%, split into two tails).
- Find the critical t-value: Based on the t-table, the t-value for 9 degrees of freedom at the 95% confidence level is approximately:
- t(0.025, 9) ≈ 2.262
So, the value of t for a 95% confidence interval with 10 data points is approximately 2.262.
In conclusion, you can use this t-value when calculating the margin of error and constructing the confidence interval for your sample mean.