A student wants to estimate the mean score of all college students for a particu
ID: 3122469 • Letter: A
Question
A student wants to estimate the mean score of all college students for a particular exam. First use the range rule of thumb to make a rough estimate of the standard deviation of those scores. Possible scores range from 800 to 2600. Use technology and the estimated standard deviation to determine the sample size corresponding to a 99% confidence level and a margin of error of 1C0 points. What isn't quite right with this exercise? The range rule of thumb estimate for the standard deviation is. A confidence level of 99% requires a mimimum sample size of. What isn't quite right with this exercise? A. A minimum sample size of 135 is not feasible to use to estimate the mean test scores. B. A margin of error of 100 points seems too high to provide a good estimate of the mean score. C. The range rule of thumb introduces too much inaccuracy for this procedure. D. These results don't apply to a test that has multiple choice questions.Explanation / Answer
The range rule of thumb states that the range is about four times the standard deviation.
s = R/4
s- standard deviation
R= Maximum- Minimum of a range.
Given: R = 2600-800 = 1800
Hence standard deviation can be calculated as:
s = R/4 = 1800/4 = 450
Deternining sample size:
1. Deviding confidence level by two , za/2= 0.99/2 = 0.495
The closest z score for 0.495 is 2.58.
2.Multiplying z score by standard deviation ,
2.58× 450 = 1161
3. Deciding it by margin of error
1161/100 = 11.61
4.Squaring it : (11.61)2= 134.79~ 135
Checking , margin of error = 1/n. [ n is the sample size]
Not feasible sample size , or the margin of error given in the question.( high)
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