Final answer:
The critical value t* for the specified confidence intervals is found using a t-distribution table or calculator function like invT, inputting the corresponding cumulative area and degrees of freedom for each case.
Step-by-step explanation:
To find the critical value t* for the given confidence intervals and degrees of freedom, one would typically use a t-distribution table or an electronic function such as invT on calculators. The critical value t* represents the cutoff points on the t-distribution curve where the area between those points and the curve represents the level of confidence we are looking for.
Finding the critical value t* for a 95% confidence interval with df=14:
For a 95% confidence interval, we are allocating 2.5% of the tail area in each end of the t-distribution (since it is two-tailed), which corresponds to a cumulative area of 0.975. Using a t-distribution table or a calculator's invT function, inputting 0.975 and df=14 would give us the critical t value.
Finding the critical value t* for a 98% confidence interval with df=7:
Similarly, for a 98% confidence interval, 1% tail area is left in each end of the distribution, thus the cumulative area used is 0.99. By inserting 0.99 and df=7 into the t-distribution table or calculator function invT, we would obtain the critical value t*.
Since the specific values are not given in the reference information, we advise using statistical software or a calculator to find the exact critical values for the confidence levels and degrees of freedom stated.