1 Solves followings Homework 4 Given the following informati

1. Solves followings.

Homework #4

Given the following information, determine the 98% confidence interval estimate of the population mean.:

x 500 , 12 , n 50

Repeat part a using a 95% confidence interval.

Repeat part a using a 90% confidence interval.

Review part a-c and discuss the effect on the confidence interval estimator of

decreasing the confidence interval.

Solves followings.

A random sample of 100 observations was randomly drawn from a population whose standard deviation is 5. The sample mean was calculated as x 400 .

Estimate the population mean with 99% confidence.

Repeatpartawith x200.

Repeat part a with x 100 .

Describe what happens to the width of the confidence interval estimate when the

sample mean decreases.

Solution

a)
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=500
Standard deviation( sd )=12
Sample Size(n)=50
Confidence Interval = [ 500 ± Z a/2 ( 12/ Sqrt ( 50) ) ]
= [ 500 - 2.33 * (1.697) , 500 + 2.33 * (1.697) ]
= [ 496.046,503.954 ]

b)
AT 95% CI
Mean(x)=500
Standard deviation( sd )=12
Sample Size(n)=50
Confidence Interval = [ 500 ± Z a/2 ( 12/ Sqrt ( 50) ) ]
= [ 500 - 1.96 * (1.697) , 500 + 1.96 * (1.697) ]
= [ 496.674,503.326 ]

c)
AT 90% C.I
Confidence Interval = [ 500 ± Z a/2 ( 12/ Sqrt ( 50) ) ]
= [ 500 - 1.64 * (1.697) , 500 + 1.64 * (1.697) ]
= [ 497.217,502.783 ]