This gives the same results as before.
This gives the same results as before.
We want the t values such that there is 95% of the area under the curve between them, symmetrically. Therefore, we use the equation solver to obtain these values from the tcdf function, which is under DISTR.
The tcdf function takes three arguments, i.e. (lower bound, upper bound, df), where df stands for degrees of freedom. We want to know the lower bound and the upper bound, but we know that one is just the negative of the other, due to the symmetry of the curve. So we can just pick one of them to solve for. For the arguments, enter L for the lower bound, U for the upper bound, and D for the degrees of freedom. Also, set the cdf equal to A, representing the area between L and U. Once these variables are entered, press ENTER. Now we need to enter actual values for the arguments. There are a few different ways we could do this. Consider the left tail area of the curve, which is .025. Let's have the calculator solve for the t critical value on the left side. So L will be negative infinity, U is what we want to solve for, D = df = n-1 = 20-1 = 19 for this problem, and A = .025. Enter in these values for L (use -1E99), D and A.
The solver expects a "guess" for U. We can simply enter "0" for this, since all t-curves are centered about zero. With the cursor on the U=0 line, press SOLVE. This is done by pressing ALPHA ENTER. The calculation will take about 20 seconds; be patient!
110 362 246 85 510 208 173 425 316 179We were not given a mean or standard deviation; we'll have to get them ourselves from the data. Of course, the standard deviation we get will be a sample standard deviation, which makes this a t-interval, as opposed to a Z-interval. Enter the data into your calculator, into L_{1}, say. Obtain the summary statistics from STAT CALC 1-Var Stats.
So for this data, we have , s = 138.8, and n = 10.
This gives the same results as before.