Question

The college board reported the following mean scores for the three parts of the sat: critical reading 502 mathematics 515 writing 494 assume that the population standard deviation on each part of the test is σ = 100. if required, round your answers to two decimal places.

(a) for a random sample of 30 test takers, what is the sampling error of x for scores on the critical reading part of the test?

(b) for a random sample of 60 test takers, what is the sampling error of x for scores on the mathematics part of the test?

(c) for a random sample of 90 test takers, what is the sampling error of x for scores on the writing part of the test?

Answer 1

The sampling error, or standard error of the mean, depends on both the population standard deviation and the size of the sample. It is calculated as the standard deviation divided by the square root of the sample size. For the respective SAT sections with sample sizes 30, 60, and 90, the sampling errors are 18.26, 12.91, and 10.54.

Step-by-step explanation:

The student is asking about sampling error, which can be calculated using the formula for the standard error of the mean (SEM) given by SEM = σ/√n, where σ is the population standard deviation and n is the sample size.

1. For the critical reading part of the SAT with a sample size of 30, the SEM can be calculated as 100/√30, which is approximately 18.26.
2. For the math part with a sample size of 60, the SEM is 100/√60, which simplifies to approximately 12.91.
3. For the writing part with a sample size of 90, the SEM is 100/√90, which simplifies to about 10.54.

In each case, the sampling error is the standard error of the mean for that section's scores.