Question

To estimate the mean score μ of those who took the Medical College Admission Test on your campus, you will obtain the scores of an SRS of students. From published information you know that the scores are approximately Normal with standard deviation about 6.5. You want your sample mean x¯ to estimate μ with an error of no more than 1.3 point in either direction.
(a) What standard deviation (±0.0001) must x¯ have so that 99.7% of all samples give an x¯ within 1.3 point of μ?

(b) How large an SRS do you need in order to reduce the standard deviation of x¯ to the value you found in part (a)?

Answer 1

Answer:

Step-by-step explanation:

Let X be the SRS scores of students.

Given that X is normal with standard deviation about 6.5.

Mean difference = $|bar x-\mu|$ is desired

i.e. Z score should be $|z|$

Std error = std deviation of sample = 0.447

b) $z =2.95\\\frac{1.3}{s} =2.95\\s = 0.447\\6.5/\sqrt{n} =0.447\\n >193$

So std error must be 0.997 and sample size must be atleast 193 to get the difference of x bar and mu to lie within 1.3 points in either direction