Say we have a sample of a large number, n, of observations from a distribution w

Question

Say we have a sample of a large number, n, of observations from a distribution with mean and say we calculate the sample mean and the sample standard deviation.

a) State the formula for a 99% confidence interval for . You may use symbols for any of the following in your answer: the mean, standard deviation, sample mean, sample standard deviation, sample size.

b) For each of the following, state if the confidence interval would be wider, narrower or the same width as

the confidence interval from part a and give a justification for your answer (note, for each of these subparts, assume that, except for the identified change, everything else is the same as in part a):

i) The sample mean was larger.

ii) The sample standard deviation was larger.

iii) The sample was larger.

iv) We calculated a 95% CI.

Explanation / Answer

A)

Note that we have a large sample size, so we can use z distribution. As c = 0.99, alpha/2 = 0.005,              
Hence, the critical z is

z = 2.576. Thus,

      
Lower Bound = X - 2.576 * s / sqrt(n)              
Upper Bound = X + 2.576 * s / sqrt(n)          

where

X = sample mean

s = sample standard deviation

n = sample size

*****************************

b)

i) The sample mean was larger.

THE SAME, as the standard error is unaffected.

ii) The sample standard deviation was larger.

WIDER, as the standard error becomes larger.

iii) The sample was larger.

NARROWER, as the standard error becomes smaller.

iv) We calculated a 95% CI.
  
NARROWER, because the critical z becomes smaller.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.