Answer:
The confidence interval for the population proportion p is between ( 0.165 and 0.335 )
Hence, Option a) 0.165 and 0.335 is the correct answer.
Step-by-step explanation:
Given the data in the question;
sample size n = 100
sample proportion p₀ = 0.25
q₀ = 1 - p₀ = 1 - 0.25 = 0.75
confidence interval = 95%
First we calculate our Standard Error
Standard Error = √( ( p₀ × q₀ ) / n )
we substitute
Standard Error = √( ( 0.25 × 0.75 ) / 100 )
Standard Error = √( 0.1875 / 100 )
Standard Error = √0.001875
Standard Error = 0.0433
Now, For 95% confidence interval; z = 1.96
so confidence interval for the population proportion p will be;
⇒ p₀ ± ( z × Standard Error )
we substitute
⇒ 0.25 ± ( 1.96 × 0.0433 )
⇒ 0.25 ± 0.084868
⇒ ( 0.25 - 0.084868 ), (0.25 + 0.084868 )
⇒ ( 0.25 - 0.084868 ), (0.25 + 0.084868 )
⇒ ( 0.165, 0.335 )
Therefore, The confidence interval for the population proportion p is between ( 0.165 and 0.335 )
Hence, Option a) 0.165 and 0.335 is the correct answer.
