Question

 

A sample of 36 students Irving College produce a mean gpa of 3.2. The standard deviation of all students is .6. Find the 95% confidence interval.

STEP 1: Find the standard deviation of the sample: .6 divided by square root of 36 = .1

STEP 2: Find the Z-score associated with 95% confidence (Go to table IV in the front of your book and find the Z-score that has .975 to the left of it. (We look for .975, because the table gives the area to the left of the Z-score [see the image at the top of the table], and if a Z-score has .975 to the left of it, it has .025 in the right tail. A confidence interval has "two tails", so the total in the tails is .025 + .025 = .05. The "inside" would be 1 - .05 = .95. The z-score is 1.96

HINT:

You can use the following numbers as guidelines for Z-scores:

Confidence Interval	Z-Score
99%	2.57
98%	2.33
95%	1.96
90%	1.65

STEP 3: Multiply the z-score and the standard deviation of the sample together: 1.96 * .1 = .196

STEP 4: Construct your confidence interval by subtracting this number from the mean (3.2-.196 = 3.04) and adding this number to the mean (3.2 +.196 = 3.396). The 95% confidence interval is 3.04 to 3.396.

Answer 1

 

A sample of 64 students Irving College produce a mean gpa of 4.0. The standard deviation of all students is .4. Find the 99% confidence interval.

STEP 1: Find the standard deviation of the sample: .4 divided by square root of 64 = .05

STEP 2: Find the Z-score associated with 99% confidence (Go to table IV in the front of your book and find the Z-score that has .995 to the left of it. (We look for .995, because the table gives the area to the left of the Z-score [see the image at the top of the table], and if a Z-score has .995 to the left of it, it has .005 in the right tail. A confidence interval has "two tails", so the total in the tails is .005 + .005 = .01. The "inside" would be 1 - .01 = .99. The z-score is 2.57

STEP 3: Multiply the z-score and the standard deviation of the sample together: 2.57 * .1 = .257

STEP 4: Construct your confidence interval by subtracting this number from the mean (4.0-.257 = 3.743) and adding this number to the mean (4.0 +.257 = 4.257). The 99% confidence interval is 3.743 to 4.257).