Mean IQ of College Professors The Wechsler IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of college professors. We want to be 99% confident that our sample mean is within 4 IQ points of the true mean. The mean for this population is clearly greater than 100. The standard deviation for this population is less than 15 because it is a group with less variation than a group randomly selected from the general population; therefore, if we use σ = 15 we are being conservative by using a value that will make the sample size at least as large as necessary. Assume then that σ = 15 and determine the required sample size. Does the sample size appear to be practical?

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Asked Jan 12, 2020
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Mean IQ of College Professors The Wechsler IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of college professors. We want to be 99% confident that our sample mean is within 4 IQ points of the true mean. The mean for this population is clearly greater than 100. The standard deviation for this population is less than 15 because it is a group with less variation than a group randomly selected from the general population; therefore, if we use σ = 15 we are being conservative by using a value that will make the sample size at least as large as necessary. Assume then that σ = 15 and determine the required sample size. Does the sample size appear to be practical?

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Expert Answer

Step 1

Critical value:

For the 99% confidence level,

Statistics homework question answer, step 1, image 1
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Step 2

Use the Table A-2 of the standard normal distribution to find z score.

  • Move left until the first column and note the value as 2.5
  • Move upward until the top row is reached and note the values as 0.07 and 0.08

The critical value is the average of the z-values 2.57 and 2.58. That is

Statistics homework question answer, step 2, image 1
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Step 3

Thus, the critical value for 99% confidence level is 2.575.

The f...

Statistics homework question answer, step 3, image 1
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