Q1
Confidence Interval - Definition
A confidence interval is random estimator of a population parameter value. It is typically computed
confidence level such that 95•/o of all possible confidence intervals cornain the true parameter value.
Confidence Interval - Confidence and significance levels
Confidence level (%o) = 100% - significance level e (%)
March
lucreasiiig the sample size
Critical value for 959a confidence level and sample size 25 for confidence interval for mean
Critical value for 90% confidence level and DF=27 Critical value for 99% confidence level for proportion
Increasing the confidence level
Increasing the sample size 2. Narrows the Confidence Interva SEE Row 5, Column AD for
the Proofl
Critical value for 95% confidence level
and sample size 25 for confidence
interval for mean 4. 2.064 2.064 T.INV.2T(0.05,24)
Critical value for 90% 5. 1.703 1.703 T.INV.2T(0.1,27)
confidence level and DF=27
Critical value for 99% 3. 2.576 2.576 NORM.S.RW(1-(0.01/2))
confidence level for proportion
Increasing the confidence level l. M idens the Confidence Interval
r SEE Row 5, Column AI for
the Proofj
Q2
Confidence Interval - Relationship of width and level
What happens if the confidence level is decreased or the s
at a 95%
The confidence interval width decreases
,at a 95%
1 Wideiis the coiifidence iiiteival
2 Narrows the confidence interval
3 2.576
4 2.064
Ii 1.703
6 Has no elléct on the width o1 the confidence interval
7 Decreases the critical value
8 L96
9
1.645
10
2.069
11
1.706
none of the above
, is typically computed
he true parameter value.
width and level
s decreased or the s
, Q5
The lower confidence limit for a poll of 87 people with proportion 0.70 in favor at 99% confidence level and 3 d Alpha
1%o 1-.99
P 0.7 Given
1 -P 0.3 1 -.7
Conf. Level 99% Given
n 87 Given
SE 0.0491304 ((0.7*0.3)/87)^0.5
Critical Value 2.5758293 NORM.S.INV(1-0.01)
ME (SE * Crit. Val} 0.126551d 0.Ot9*2.576
Lower Confidence Limit 0.573 0.7 - 0.127
Confidence Level and \V
Confidence Level
Sample Size
Degrees of Freedom Critical Value
(T-Stat) X Bar
Standard Deviation
Standard Error Margin of Error
Upper Bound Lower Bound
Range of Width
As the. CO!!k • e. les e’.1 iS ale.c
inrre‹is ed, the ›i idtli of the in
Confidence Interval - Definition
A confidence interval is random estimator of a population parameter value. It is typically computed
confidence level such that 95•/o of all possible confidence intervals cornain the true parameter value.
Confidence Interval - Confidence and significance levels
Confidence level (%o) = 100% - significance level e (%)
March
lucreasiiig the sample size
Critical value for 959a confidence level and sample size 25 for confidence interval for mean
Critical value for 90% confidence level and DF=27 Critical value for 99% confidence level for proportion
Increasing the confidence level
Increasing the sample size 2. Narrows the Confidence Interva SEE Row 5, Column AD for
the Proofl
Critical value for 95% confidence level
and sample size 25 for confidence
interval for mean 4. 2.064 2.064 T.INV.2T(0.05,24)
Critical value for 90% 5. 1.703 1.703 T.INV.2T(0.1,27)
confidence level and DF=27
Critical value for 99% 3. 2.576 2.576 NORM.S.RW(1-(0.01/2))
confidence level for proportion
Increasing the confidence level l. M idens the Confidence Interval
r SEE Row 5, Column AI for
the Proofj
Q2
Confidence Interval - Relationship of width and level
What happens if the confidence level is decreased or the s
at a 95%
The confidence interval width decreases
,at a 95%
1 Wideiis the coiifidence iiiteival
2 Narrows the confidence interval
3 2.576
4 2.064
Ii 1.703
6 Has no elléct on the width o1 the confidence interval
7 Decreases the critical value
8 L96
9
1.645
10
2.069
11
1.706
none of the above
, is typically computed
he true parameter value.
width and level
s decreased or the s
, Q5
The lower confidence limit for a poll of 87 people with proportion 0.70 in favor at 99% confidence level and 3 d Alpha
1%o 1-.99
P 0.7 Given
1 -P 0.3 1 -.7
Conf. Level 99% Given
n 87 Given
SE 0.0491304 ((0.7*0.3)/87)^0.5
Critical Value 2.5758293 NORM.S.INV(1-0.01)
ME (SE * Crit. Val} 0.126551d 0.Ot9*2.576
Lower Confidence Limit 0.573 0.7 - 0.127
Confidence Level and \V
Confidence Level
Sample Size
Degrees of Freedom Critical Value
(T-Stat) X Bar
Standard Deviation
Standard Error Margin of Error
Upper Bound Lower Bound
Range of Width
As the. CO!!k • e. les e’.1 iS ale.c
inrre‹is ed, the ›i idtli of the in