Answer to Question #150175 in Statistics and Probability for caarino

Question

a. From the information given here determine the
95% confidence interval estimate of the population
mean.
x = 100  = 20 n = 25
b. Repeat part (a) with x = 200.
c. Repeat part (a) with x = 500.
d. Describe what happens to the width of the confidence
interval estimate when the sample mean
increases.

Answer 1

95 % CI=$\bar x±Z_\frac{\alpha}{2}\frac{\sigma}{\sqrt n}$

a) $\bar x=100$

=$100±1.96* \frac {20}{\sqrt{25}}$

=(92.16, 107.84)

b)$\bar x=200$

$=200±1.96* \frac {20}{\sqrt{25}}$

=(192.16, 207.84)

c) $\bar x=500$

=$500±1.96* \frac {20}{\sqrt{25}}$

=(492.16, 507.84)

d) As the sample mean increases the confidence interval width remains constant. This is because the standard error is constant for all sample means.