Question

An IQ test is designed so that the mean is 100 and the standard deviation is 12 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 90​% confidence that the sample mean is within 33 IQ points of the true mean. Assume that σ=12 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

Answer 1

Answer:

Sample size = 1

Not a reasonable sample size

Step-by-step explanation:

Mean of the test scores = u = 100

Standard deviation of the test scores = σ = 12

Confidence Level = 90%

The z-score for 90% confidence level = z = 1.645

Mean IQ should be 33 points within the sample mean. So,

Error size = E = 33

Sample size = n ?

Since the distribution is normal, we can use the formula of margin of error for z-distribution to calculate the missing sample size.

$E = z\frac{\sigma}{\sqrt{n} } \\\\\sqrt{n}= \frac{z \sigma}{E}$

$n=(\frac{z \sigma}{E})^{2}$

Using the given values, we get:

$n=(\frac{12 \times 1.645}{33} )^{2}\\\\ n = 0.357$

Rounding to the next bigger integer the sample size comes out to be 1. This is not a reasonable estimate for a real world calculation as we cannot draw a conclusion for a complete population based on the sample size of 1 person

Answer 2

The required sample size using technolog is 0.3578. No. This number of IQ test scores is a fairly small number.

Required sample size

Using this formula

Required Sample Size = (Z-score× StdDev / (margin of error))²

Where:

Standard deviation=12

Margin of Error = 33

z-score for a 90% confidence level= 1.645

Let plug in the formula

Required Sample Size = (1.645 × 12 / 33)²

Required Sample Size = 0.3578

Based on the above required sample size the sample size is not reasonable for a real world calculation beacuse this number of IQ test scores is a fairly small number.

Inconclusion the required sample size using technolog is 0.3578.

Learn more about required sample size here:https://brainly.com/question/17203075