Question

A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is σ = 15. a. Compute the 95% confidence interval for the population mean. b. Assume that the same sample mean was obtained from a sample of 120 times. Provide a 95% confidence interval for the population mean. c. What is the effect of a larger sample size on the interval estimate?

Answer 1

Answer:

a) (76.21,83.79)

b) (77.32,82.68)    

c) Interval decreases    

Step-by-step explanation:

We are given the following information in the question:

Sample size, n = 60

Sample mean = 80

Sample standard Deviation, s = 15

a) 95% Confidence interval:

$\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}$

Putting the values, we get,

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

$80 \pm 1.96(\dfrac{15}{\sqrt{60}} ) = 80 \pm 3.79 = (76.21,83.79)$

b) Sample size, n = 120

95% Confidence interval:

$80 \pm 1.96(\dfrac{15}{\sqrt{120}} ) = 80 \pm 2.68 = (77.32,82.68)$

c) As observed increasing the sample size, the confidence interval become smaller.