A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean mathematics SAT score to be 459. Assume the population standard deviation is o = 116. Construct a 90% confidence interval for the mean mathematics SAT score for the entering freshman class. Round the answer to the nearest whole number. < A 90% confidence interval for the mean mathematics SAT score is.

The 90% confidence interval for the SAT score is between 440 and 478.

mean (μ) = 459, standard deviation (σ) = 116, sample (n) = 100, confidence = 90% = 0.90

α = 1 - C = 1 - 0.90 = 0.1

α/2 = 0.1/2 = 0.05

The z score of α/2 is equal to the z score of 0.45 (0.5 - 0.05) which is equal to 1.645.

The margin of error (E) is given by:

The confidence interval = μ ± E = 459 ± 19 = (440, 478)

The 90% confidence interval for the SAT score is between 440 and 478.

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A 90% confidence interval for the mean mathematics SAT score is (440, 478).

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 459 - 19 = 440

The upper end of the interval is the sample mean added to M. So it is 459 + 19 = 478

A 90% confidence interval for the mean mathematics SAT score is (440, 478).

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