Question
In: Statistics and Probability
A city has located in a specific geographic area. It has several snowy days. On 76...
A city has located in a specific geographic area. It has several snowy days. On 76 of 350 randomly selected days, it snows. Find a 99% confidence interval for the true proportion of days on which it snows.
Solutions
Expert Solution
Solution :
Given that,
n = 350
x = 76
Point estimate = sample proportion = 
= x / n = 76/350=0.217
1 -
= 1-0.217 =0.783
At 99% confidence level the z is ,
= 1 - 99% = 1 - 0.99 =
0.01
/ 2 = 0.01 / 2 = 0.005
Z/2
= Z0.005 = 2.576 ( Using z table )
Margin of error = E = Z
/2 *
(
* (1 -
)) / n)
= 2.576* (
= 0.057
99% confidence interval for the true proportion,is
- E < p <
+ E
0.217 - 0.057 < p < 0.217 + 0.057
0.160< p < 0.274
(0.16 ,0.274)
The 99% confidence interval for the population proportion p is :
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