The standard IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of all adults. We wish to find the sample size necessary to estimate the mean IQ score of all people who have successfully passed a college statistics course. We want to create a confidence interval that is no wider than 8 IQ points. The standard deviation for this sub-population is certainly less than 15 as it should be a less variable population. Therefore by using σσ = 15 we will obtain a conservative sample size, meaning it will be sufficient large enough. How large a sample should we utilize for a 95% confidence interval? (use the z-score 1.95996 )

Accepted Solution

Answer:55 people is the minimum sample sizeStep-by-step explanation:The formula for minimum sample size is  for µ is:  n = [(z*σ)/E]²We are given z = 1.95996, σ = 15 and E = 4E is 4 because they said they want the interval no wider than 8, so that means 4 lower and 4 higher than the mean, so E is 4Calculate:  n = [(1.95996*15)/4]² = 54.02, we always round up when talking about people.  Since 54.02 is the score, we need more than 54 people, since we can't have parts of a person, we need to round up to 55