Answer:
Step 1 z(c) = 2,323
CI = ( 25 ; 30,2 )
Step-by-step explanation:
Normal Distribution:
Sample size n = 25
Sample mean μ = 27,6
Sample standard deviation s = 5,69
CI = 98 % then α = 1 - 0,98 α = 0,02 α/2 = 0,01
From z-table we don´t find z (score) for 0,01 directly, we need to interpolate between z = 2,32 and z = 2,33
For 0,0099 z score is 2,33
for 0,0102 z score is 2,32
Δ 0,0003 0,01
Then by rule of three
for Δ 0,0003 ⇒ 0,01
for Δ (0,01- 0,0102) ⇒ x
0,0003 0,01
0,0002 x
x = 0,0067
then z (score for 0,01) = 2,33 - 0,0067 z(c) = 2,3233
round to three decimal places z(c) = 2,323
Step 2:
CI = μ ± z(c) * s/√n ⇒ 27,6 ± (2,323 * 5,69)/5
CI = 27,6 ± 2,6436
round to one decimal place
CI = 27,6 ± 2,6
CI = ( 25 ; 30,2 )
