Click OK to display the result under \"conf Sample Size Determination Not availa
ID: 3360152 • Letter: C
Question
Click OK to display the result under "conf Sample Size Determination Not available. Basic Skills and Concepts tat tistical Literacy and Critical Thinking Results in the Media USA To day provided results from a poll of 1000 adults who were 1 poto identify their favor te pie. Among the 100 respondents 14% chose chocolate pie, and n of error was given as ±4 percentage points. what important feature of the poll was the margi omitted? argin of Error For the poll described in Exercise 1. describe what is meant by the state- hat "the margin of error was given as ±4 percentage points otation For the poll described in Exerise lwhat values do p q n E, and p represent? If the confidence level is 95% 4. Confidence Levels Given specific sample data, such as the data given in Exercise 1, which is it wider? confidence Interval is wider: the 95% confidence interval or the 80%confidence interval, why , what is the value of ? Finding Critical Values. In Exercises 5-8, find the critical value zap that corresponds to the given confidence level. 5.90% 6.99% 7.99.5% 8.98% Formats of Confidence Intervals. In Exercises 9-12, express the confidence interval using the indicated format. (The confidence intervals are based on the proportions of red orange, yellow, and blue M&Ms; in Data Set 27 "M&M; Weights" in Appendix B.) 9. Red M&Ms; Express 0.0434Explanation / Answer
1)
TRADITIONAL METHOD
given that,
possibile chances (x)=140
sample size(n)=1000
success rate ( p )= x/n = 0.14
I.
sample proportion = 0.14
standard error = Sqrt ( (0.14*0.86) /1000) )
= 0.011
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
margin of error = 1.96 * 0.011
= 0.0215
III.
CI = [ p ± margin of error ]
confidence interval = [0.14 ± 0.0215]
= [ 0.1185 , 0.1615]
-----------------------------------------------------------------------------------------------
DIRECT METHOD
given that,
possibile chances (x)=140
sample size(n)=1000
success rate ( p )= x/n = 0.14
CI = confidence interval
confidence interval = [ 0.14 ± 1.96 * Sqrt ( (0.14*0.86) /1000) ) ]
= [0.14 - 1.96 * Sqrt ( (0.14*0.86) /1000) , 0.14 + 1.96 * Sqrt ( (0.14*0.86) /1000) ]
= [0.1185 , 0.1615]
-----------------------------------------------------------------------------------------------
interpretations:
1. We are 95% sure that the interval [ 0.1185 , 0.1615] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population proportion
2)
TRADITIONAL METHOD
given that,
possibile chances (x)=140
sample size(n)=1000
success rate ( p )= x/n = 0.14
I.
sample proportion = 0.14
standard error = Sqrt ( (0.14*0.86) /1000) )
= 0.011
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.2
from standard normal table, two tailed z /2 =1.282
margin of error = 1.282 * 0.011
= 0.0141
III.
CI = [ p ± margin of error ]
confidence interval = [0.14 ± 0.0141]
= [ 0.1259 , 0.1541]
-----------------------------------------------------------------------------------------------
DIRECT METHOD
given that,
possibile chances (x)=140
sample size(n)=1000
success rate ( p )= x/n = 0.14
CI = confidence interval
confidence interval = [ 0.14 ± 1.282 * Sqrt ( (0.14*0.86) /1000) ) ]
= [0.14 - 1.282 * Sqrt ( (0.14*0.86) /1000) , 0.14 + 1.282 * Sqrt ( (0.14*0.86) /1000) ]
= [0.1259 , 0.1541]
-----------------------------------------------------------------------------------------------
interpretations:
1. We are 80% sure that the interval [ 0.1259 , 0.1541] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 80% of these intervals will contains the true population proportion
3.level of significance, = 0.05 because 95% confidence interval
4) We are 95% sure that the interval [ 0.1185 , 0.1615] and We are 80% sure that the interval ( 0.1259 , 0.1541) so that 80% confidence interval is wider than 95% confidence
5)90%
Critical Value
The Value of Z at 0.1 LOS is +1.6449 and -1.6449
6)99%
Critical Value
The Value of Z at 0.01 LOS is +2.5758 and -2.5758
7)99.5%
Critical Value
The Value of Z at 0.5 LOS is +0.6745 and -0.6745
8)98%
Critical Value
The Value of Z at 0.02 LOS is +2.3263 and -2.3263
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