Please come up with a word problem using the example below as a guide. A sample

Question

Please come up with a word problem using the example below as a guide.

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.

Confidence Interval

Z-Score

99%

2.57

98%

2.33

95%

1.96

90%

1.65

Explanation / Answer

So, you want another word problem of a similar kind. Here' the answer:

Q: A sample of 100 people have a mean height of 180 cm. The standard deviation is 10 cm. Find the 99% confidence interval

To solve the problem you use the same formula:

Mean +/- Z*Stdev/sqrt(n)

= 180 +/- 2.57*10/sqrt(100)

= 177.43cm to 182.57cm

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