Download Interval Estimation

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!!