PART 1 Given x 63 Sx 12 n 100 Construct a confidence inter

PART 1 Given: x = 63, Sx = 12, n =100. Construct a confidence interval of x according to:

(a) C = .95

(b) C = .99

PART 2 Repeat parts (a) and (b) of PART 1, but with the condition that n is four times as large.

Solution

PART 1.
a. AT 0.95
Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=63
Standard deviation( sd )=12
Sample Size(n)=100
Confidence Interval = [ 63 ± t a/2 ( 12/ Sqrt ( 100) ) ]
= [ 63 - 1.98 * (1.2) , 63 + 1.98 * (1.2) ]
= [ 60.624,65.376 ]

b. AT 0.99
Confidence Interval = [ 63 ± t a/2 ( 12/ Sqrt ( 100) ) ]
= [ 63 - 2.63 * (1.2) , 63 + 2.63 * (1.2) ]
= [ 59.844,66.156 ]

PART II.
a.
Confidence Interval = [ 63 ± t a/2 ( 12/ Sqrt ( 400) ) ]
= [ 63 - 1.97 * (0.6) , 63 + 1.97 * (0.6) ]
= [ 61.818,64.182 ]

b.
Confidence Interval = [ 63 ± t a/2 ( 12/ Sqrt ( 400) ) ]
= [ 63 - 2.59 * (0.6) , 63 + 2.59 * (0.6) ]
= [ 61.446,64.554 ]