Final answer:
The critical t-value for a 98% confidence interval when the sample size is 15 is found by using the degrees of freedom (df = 14) and searching for the t-value that corresponds to the 99th percentile (1 - 0.01) of the t-distribution. It can be obtained via tables or an 'invT' function in statistical software and should be rounded to four decimal places.
Step-by-step explanation:
To find the critical t-value for a 98% confidence interval when the sample size is 15, we first need to determine the degrees of freedom (df). This is the sample size minus 1, so in this case, df = 15 - 1 = 14. Since we are working with a two-sided 98% confidence interval, we are looking for the t-value that puts 1% in the upper tail (since the total area in the tails is 2%, and it is divided equally between the upper and lower tails in a two-sided test).
You can find this critical t-value using a t-distribution table or an online calculator/function such as 'invT' or similar in statistical software. The function typically requires the area to the left of the critical value, which would be 1 - 0.01 = 0.99 in this case. The resulting critical t-value should then be rounded to four decimal places as per the question's requirement.