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INTERVAL ESTIMATION FOR POPULATION MEAN: SIGMA ( ) UNKNOWN. You can find the problem we are going to solve here on page 314 of your textbook. 14. A simple random sample with n=54 provided a sample mean of 22.5 and a sample standard deviation of 4.4. B. Develop a 95% confidence interval for the population mean. Solution. B. We know that the margin of error is found using the following formula: s t n 2 Thus, in order to find the margin of error we need to find t first. Since we want a confidence level of 2 95% this implies that Finding = 5%, which means that 2 = 0.025. t 0.025 using a Table. Step 1. Go to page 920, we know that d.f. = n -1 = 53. Step 2. Find 53 on the first column of Table 2 (page 921). Step 3. Find 0.025 on the first row of Table 2 (page 921). Step 4. t 0.025 2.006 Now, we can compute the margin of error: s t 2.006(4.4 / 54 ) 1.2011 2 n Finally, we know that a confidence interval for the population mean, when sigma is unknown, can be found with the following formula: s x t 22.5 2.006(4.4 / 54 ) 22.5 1.2011 (21.2989,23.7011) 2 n FINDING THE SAME CONFIDENCE INTERVAL USING A TI-83. Step 1. Press STAT. Step 2. Go to TESTS. Step3. Go to TInterval and press ENTER. Step 4. Highlight Stats and press ENTER Step 5. Plug in the values of s , x , n and the confidence level. Step 6. Highlight Calculate and press ENTER. You should see something like this. We are done!!