Question

1. One hundred people are included in a study in which they are compared to a known population that has a mean of 73, a standard deviation of 20, and a rectangular distribution.

1. μM = __________.
2. σM = __________.
3. The shape of the comparison distribution is __________.
4. If the sample mean is 75, the lower limit for the 99% confidence interval is __________.
5. If the sample mean is 75, the upper limit for the 99% confidence interval is __________.
6. If the sample mean is 75, the lower limit for the 95% confidence interval is __________.
7. If the sample mean is 75, the upper limit for the 95% confidence interval is __________.

Answer 1

a)

M = = 73

b)

M = / sqrt(n) = 20 / sqrt(100) = 2

c)

Since sample size 100 is sufficiently large ( n > 30) , the shape of distribution is approximately normal.

d)

Lower limit for 99% confidence interval is = - Z/2 * M  

= 75 - 2.576 * 2

= 69.848

e)

Upper limit for 99% confidence interval is = + Z/2 * M  

= 75 + 2.576 * 2

= 80.152

f)

Lower limit for 95% confidence interval is = - Z/2 * M  

= 75 - 1.96 * 2

= 71.08

g)

Upper limit for 95% confidence interval is = + Z/2 * M  

= 75 + 1.96 * 2

= 78.92