An IQ test is designed so that the mean is 100 and the standard deviation is 14 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 7 IQ points of the true mean. Assume that o = 14 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 (Round up to the nearest integer.)

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### Sample Size Determination for IQ Test Analysis

**Problem Statement:**

An IQ test is designed with the following parameters:
- Mean (μ) = 100
- Standard deviation (σ) = 14

The objective is to find the sample size necessary to estimate the mean IQ score of statistics students. The estimate should have a 95% confidence interval with a margin of error of 7 IQ points from the true mean. Assume that σ = 14. Use these parameters to determine the required sample size with the help of technology and analyze if this is a feasible sample size for real-world calculations.

**Task:**
- Find the required sample size and round up to the nearest integer.

**Instructions:**
- Enter your answer in the provided answer box.
- Click "Check Answer" to see if your solution is correct.
- You have 1 attempt remaining.

**Note:**
This exercise helps to understand the application of sample size determination in estimating population means with specified confidence and precision.
Transcribed Image Text:### Sample Size Determination for IQ Test Analysis **Problem Statement:** An IQ test is designed with the following parameters: - Mean (μ) = 100 - Standard deviation (σ) = 14 The objective is to find the sample size necessary to estimate the mean IQ score of statistics students. The estimate should have a 95% confidence interval with a margin of error of 7 IQ points from the true mean. Assume that σ = 14. Use these parameters to determine the required sample size with the help of technology and analyze if this is a feasible sample size for real-world calculations. **Task:** - Find the required sample size and round up to the nearest integer. **Instructions:** - Enter your answer in the provided answer box. - Click "Check Answer" to see if your solution is correct. - You have 1 attempt remaining. **Note:** This exercise helps to understand the application of sample size determination in estimating population means with specified confidence and precision.
Expert Solution
Step 1

Solution:

From the given information, the E=7 and σ=14.

The confidence level is 0.95.

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