An educational researcher is interested in estimating the average GPA of all LSU students. The GPA is collected from 150 random students. A 98% confidence interval for μ is: (2.71, 3.01).

What is the margin of error?

Answer:

Step-by-step explanation:

To find the margin of error, we need to know the sample mean, the confidence level, and the sample size.

The formula for the margin of error is:

Margin of Error = (Z-score) x (standard error)

where the Z-score is based on the confidence level, and the standard error is the standard deviation of the sampling distribution of the mean.

Since we are given the confidence interval, we can find the sample mean by taking the average of the two endpoints:

sample mean = (2.71 + 3.01) / 2 = 2.86

We are told that the confidence level is 98%, so the corresponding Z-score can be found using a Z-table or a calculator. For a 98% confidence level, the Z-score is approximately 2.33.

To find the standard error, we can use the formula:

standard error = (standard deviation) / sqrt(sample size)

Since we do not know the population standard deviation, we will use the sample standard deviation as an estimate. We are not given the sample standard deviation, so we cannot calculate it directly. 

However, we can use the fact that the confidence interval is:

(sample mean) ± (margin of error)

to solve for the margin of error and then use that to find the standard error.

(sample mean) + (margin of error) = 3.01 (sample mean) - (margin of error) = 2.71

Adding the two equations together, we get:

2 x (sample mean) = 5.72

Solving for the sample mean, we get:

sample mean = 2.86

Substituting this value back into one of the equations, we get:

(margin of error) = (3.01 - 2.86) / 2 = 0.075

Finally, we can find the margin of error by multiplying the Z-score by the standard error:

Margin of Error = (Z-score) x (standard error)

Standard error = (standard deviation) / sqrt(sample size)

Margin of Error = Z-score x (standard deviation / sqrt(sample size))

Margin of Error = 2.33 x (0.075 / sqrt(150))

Margin of Error ≈ 0.02

Therefore, the margin of error is approximately 0.02