Question

Suppose math SAT scores for students are normally distributed and have a known population standard deviation of 118 and an unknown population mean. A random sample of 40 students is tested and yields a sample mean of a 514 math SAT score. Find the confidence interval for the population mean with a 90% confidence level.

z₀.₁₀=1.282
z₀.₀₅ = 1.645
z₀.₀₂₅ = 1.960
z₀.₀₁ = 2.326
z₀.₀₀₅ = 5.276

Answer 1

To find the 90% confidence interval for the SAT math scores with a sample mean of 514, a population standard deviation of 118, and a sample size of 40, we get a confidence interval between 490.101 and 537.899.

Step-by-step explanation:

To calculate the confidence interval for the population mean with a known standard deviation, you would use the following formula:

Confidence Interval = Sample Mean ± (z* x Standard Error)

Where:

• Standard Error = Population Standard Deviation / √ Sample Size
• z* is the z-score corresponding to the desired confidence level

In this case, the population standard deviation (σ) is 118, the sample mean (μ) is 514, and the sample size (n) is 40.

For a 90% confidence interval, the z-score is 1.282.

First, calculate the standard error:

Standard Error = 118 / √40

= 18.649

Then, calculate the margin of error:

Margin of Error = 1.282 x 18.649

= 23.899

Now, construct the confidence interval:

Confidence Interval = 514 ± 23.899

This gives us:

Lower Limit = 514 - 23.899

= 490.101

Upper Limit = 514 + 23.899

= 537.899

Hence, we are 90 percent confident that the true population mean SAT math score lies between 490.101 and 537.899.