# Confidence Interval

*label*Mathematics

*timer*Asked: Apr 4th, 2017

*account_balance_wallet*$10

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Confidence Interval using excel

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Running Head: Confidence Interval

1

Confidence Interval:

Student’s Name:

Course Title:

University Affiliation:

Date:

Confidence Interval

2

For 90%(0.9)

𝒫’=X/n = 11/20 =0.55

The level of the significance =𝛼 =1 – confidence

1-0.9 =0.1

Critical z -Value =Z 𝛼/2 =Z 0.1/2 =Z 0.05 = 1.625 As per the Z table and doing interporation

for the value is between 1.64 and 1.65

The standard error for 𝒫’:SE =√ 𝒫’ ×(1- 𝒫’)/n

√(0.55×0.45/20)

≈ 0.111243

E = Z 𝛼/2×√ 𝒫’ ×(1- 𝒫’)/n

= 1.625 ×0.111243

≈ 0.182995

The Margin error of E = 0.183

For the 90% interval is then 0.55±𝑜. 182995

The lower limit is 0.55−0.182995 ≈ 0.367005 while the upper is

0.55+0.182995 ≈ 0.1732995

Finding sample mean and standard deviation

Mean (x’) =Σ

(𝑥)

𝑛

= 182.9/20 =9.145

Variance of the sample S2 = Σ

(𝑥−𝑥′)

𝑛−1

=40.5085/19 = 2.132079

Confidence Interval

3

Standard deviation s =√ S2 ==√ 2.132079

=1.460

95% applying Normal distribution.(0.95)

Mean of the sample x’ =9.145

𝜎 = 1.460164

n =20

The level of the significance=...

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