https://file.aiquickdraw.com/mathbot/file/1730250279279bm376kx4.jpg

To find the standard error (Part 3 of 6) in this scenario, we use the formula:

\[
\text{Standard Error} = \frac{\sigma}{\sqrt{n}}
\]

where:
- \(\sigma = 10\) (the population standard deviation),
- \(n = 76\) (the sample size).

### Calculation:
\[
\text{Standard Error} = \frac{10}{\sqrt{76}} \approx \frac{10}{8.7178} \approx 1.1456
\]

So, the standard error, rounded to four decimal places, is **1.1456**.

Would you like further details or have any questions?

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### Related Questions:
1. What is the formula for constructing a confidence interval for the mean?
2. Why is a critical value of 1.645 used for a 90% confidence level?
3. How would the standard error change with a larger sample size?
4. How does knowing the population standard deviation (as opposed to the sample) impact the calculation?
5. What would be the steps if you were calculating a 95% confidence interval instead?

### Tip:
Remember, the standard error decreases as the sample size increases, improving the precision of your confidence interval.

In IQ test was given to a simple random sample of 76 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of σ = 10. It is desired to construct a 90% confidence interval for the mean IQ score of students at this college.

Learn how to calculate a 90% confidence interval for the mean IQ score of students at a college based on a sample mean of 105.2, a standard deviation of 10, and a sample size of 76. This example covers key statistical concepts, including standard error and critical values.

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