Two hundred fish caught in Cay
Two hundred fish caught in Cayuga Lake had a mean length of 13.8inches. The population standard deviation is 3.8 inches. (Give youranswer correct to two decimal places.)
(a) Find the 90% confidence interval for the population meanlength.
| Lower Limit | |
| Upper Limit |
(b) Find the 98% confidence interval for the population meanlength.
| Lower Limit | |
| Upper Limit |
Answer:
Solution:-
Given that,
= 13.8
= 3.8
n = 200
A ) At 90% confidence level the z is ,
=1 – 90% = 1 – 0.90 = 0.10
/ 2 = 0.10 / 2 = 0.05
Z/2= Z0.05 = 1.645
Margin of error = E = Z/2*(
= 1.645 * (3.8 /
At 95% confidence interval estimate of the population meanis,
– E < 
< + E
13.8 – 0.442< < 13.8 + 0.442
13.36 < <14.24
(13.36 , 14.24)
Lower limit – 13.36
Upper limit – 14.24
b) At 98% confidence level the z is ,
=1 – 98% = 1 – 0.98 = 0.02
/ 2 = 0.02 / 2 = 0.01
Z/2= Z0.01 = 2.326
Margin of error = E = Z/2*(
= 1.326 * (3.8 /
At 98% confidence interval estimate of the population meanis,
– E < < + E
13.8 – 0.625 < < 13.8 + 0.625
13.18 < < 14.42
(13.18 , 14.42)
Lower limit – 13.18
Upper limit – 14.42
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