Question

MATH Hosted by ALEKS Corp 8.3 Homework Previous 2 3 4 5 6 7 8 9 10 Next Question 2 of 10 (1 point) View problem in a pop-up 8.3 Section Exercise 19 (calc) Smart phone: Among 248 cell phone owners aged 18-24 surveyed, 104 said their phone was an Android phone. Chec S Guide Part 1 Find a point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone. Round the answer to three decimal places. The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is .419 Show Ask My Link to Tal Forn Part 2 out of 3 Construct a 99.5% confidence interval for the proportion of cell phone owners aged 18-24 who have an Android phone. Round the answer to three decimal places. A 99.5% confidence interval for the proportion of cell phone owners aged 18-24 who have an Android phone is Save fa р Sub Assign HEC NEXT

Answer 1

2.

TRADITIONAL METHOD
given that,
possible chances (x)=104
sample size(n)=248
success rate ( p )= x/n = 0.419
I.
sample proportion = 0.419
standard error = Sqrt ( (0.419*0.581) /248) )
= 0.031
II.
margin of error = Z a/2 * (standard error)
where,
Za/2 = Z-table value
level of significance, α = 0.005
from standard normal table, two tailed z α/2 =2.807
margin of error = 2.807 * 0.031
= 0.088
III.
CI = [ p ± margin of error ]
confidence interval = [0.419 ± 0.088]
= [ 0.331 , 0.507]
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DIRECT METHOD
given that,
possible chances (x)=104
sample size(n)=248
success rate ( p )= x/n = 0.419
CI = confidence interval
confidence interval = [ 0.419 ± 2.807 * Sqrt ( (0.419*0.581) /248) ) ]
= [0.419 - 2.807 * Sqrt ( (0.419*0.581) /248) , 0.419 + 2.807 * Sqrt ( (0.419*0.581) /248) ]
= [0.331 , 0.507]
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interpretations:
1. We are 99.5% sure that the interval [ 0.331 , 0.507] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 99.5% of these intervals will contains the true population proportion