Question

an iq test is designed so that the mean is 100 and the standard deviation is 19 for the population of normal adults. find the sample size necessary to estimate the mean iq score of statistics students such that it can be said with 95% confidence that the sample mean is within 8 iq points of the true mean. assume that ( sigma = 19 ) and determine the required sample size using technology. then determine if this is a reasonable sample size for a real - world calculation.
the required sample size is 22. (round up to the nearest integer.)
would it be reasonable to sample this number of students?
no. this number of iq test scores is a fairly large number.
yes. this number of iq test scores is a fairly small number.
yes. this number of iq test scores is a fairly small number.
no. this number of iq test scores is a fairly small number.

Explanation:

Step1: Analyze the sample size

The sample size is \(n = 22\). In real - world sampling for statistical studies (especially when dealing with human subjects like students for IQ tests), a sample size of 22 is relatively small. For example, in many educational or psychological research studies, larger sample sizes (often \(n\geq30\) as a rough rule - of - thumb for the Central Limit Theorem approximation to hold well for non - normal populations, but also considering practical representativeness) are preferred. However, if the sampling process is well - designed (e.g., random sampling, proper stratification if applicable), a sample size of 22 may still be feasible. But in terms of the description of the number itself, 22 is a small number compared to what could be obtained in a school or a large group of students.

Step2: Evaluate the options

• Option 1: "No. This number of IQ test scores is a fairly large number" is incorrect because 22 is not a large number.
• Option 2: "Yes. This number of IQ test scores is a fairly small number" is correct as 22 is a small number in the context of sampling students for an IQ - related study.
• Option 3: "No. This number of IQ test scores is a fairly small number" has an incorrect "No" response.
• Option 4: "Yes. This number of IQ test scores is a fairly large number" is wrong since 22 is not large.

Answer:

Yes. This number of IQ test scores is a fairly small number.