Problem 1 (Compute CI for small sample using t-distribution given sample statistics). From a population of normally distributed IQ scores, a random sample of 25 scores yields sample mean as _X = 98:4 and sample deviation Sx = 14:2. Find a 98% con_dence interval for the true mean score _ of this population. Use Excel's TINV function to obtain your answer.
Problem 2 (Compute CI using t-distribution given raw data). Standardized test scores are often found to be normally distributed. The data set below is a random sample of combined SAT scores from a group of sophomores picked from a random university. Compute the sample mean, sample deviation and _nd a 95% con_dence interval for the mean SAT score of sophomores at this university.
1270 1110 1280 970 720 1350 1070
1220 1220 1020 1210 1170 910 1320
1160 1150 880 1030 1070 1120
950 1440 1080 1020 860 980
1070 850 1200 1400 920 800
Use Excel's TINV function to obtain your answer.
Problem 3 (Compare CI using z-score and t-score). A random sample of size 400 from a normally distributed population yields _X = 980:5 and Sx = 56:3. Compare the results of _nding a 99% con_dence interval for _ when using z-scores rather than t-scores. Use Excel's TINV and NORMINV functions to obtain your answer.