What Is The Value Of The T Score For A 99% Confidence Interval If We Take A Sample Of Size 18?

Confidence intervals estimate population parameters, such as the population hateful, by using statistics (for instance, the sample mean) plus or minus a margin of fault (MOE). To compute the margin of error for a conviction interval, you need a critical value (the number of standard errors you add and subtract to get the margin of error yous desire).

When the sample size is large (at to the lowest degree 30), or you lot know its standard deviation, you lot typically use critical values on the Z-distribution to build the margin of error. When the sample size is small (less than 30) and/or the population standard deviation is unknown, you use the t-distribution to find critical values. (At roughly 25 or 30 degrees of freedom, the values of the t-distribution begin to match those of the Z-distribution. Then, a sample size of xxx is not an must-have requirement, but information technology'll work well in many situations.)

t-table

To help you find disquisitional values for the t-distribution, you lot tin employ the last row of the t-table, which lists common confidence levels, such every bit 80%, 90%, and 95%. To find a critical value, wait up your confidence level in the bottom row of the table; this tells you lot which cavalcade of the t-table y'all need. Intersect this column with the row for your df (degrees of freedom). The number you come across is the disquisitional value (or the t-value) for your confidence interval. For example, if yous want a t-value for a 90% conviction interval when yous have 9 degrees of freedom, go to the bottom of the table, find the column for xc%, and intersect information technology with the row for df = nine. This gives yous a t -value of ane.833 (rounded).

Beyond the top row of the t-table, you run across correct-tail probabilities for the t-distribution. Simply confidence intervals involve both left- and right-tail probabilities (because you lot add and subtract the margin of mistake). And then half of the probability left from the confidence interval goes into each tail. You need to take that into account. For example, a t-value for a ninety% confidence interval has v% for its greater-than probability and five% for its less-than probability (taking 100% minus 90% and dividing by 2). Using the elevation row of the t-table, you would accept to look for 0.05 (rather than 10%, every bit you might exist inclined to practise.) But using the bottom row of the table, yous but look for 90%. (The result you lot get using either method ends up existence in the same cavalcade.)

When looking for t-values for conviction intervals, use the bottom row of the t-tabular array as your guide, rather than the headings at the top of the table.