Question

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__________.

Answer 1

Answer:

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

Step-by-step explanation:

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

$\alpha = \frac{1-0.9}{2} = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$.

So it is z with a pvalue of $1-0.05 = 0.95$, so $z = 1.645$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

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

$M = 1.645*\frac{116}{100} = 19$

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).

Answer 2

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:

$E=z_\frac{\alpha}{2} *\frac{\sigma}{\sqrt{n} } \\\\E=1.645*\frac{116}{\sqrt{100} } =19$

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

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

Find out more at: brainly.com/question/10501147