Confidence Interval

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Confidence Interval using excel

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For each of the 2 majors consider the ‘School Type’ column. Assuming the requirements are met, construct a 90% confidence interval for the proportion of the schools that are ‘Private’. Be sure to interpret your results. For each of the 2 majors construct a 95% confidence interval for the mean of the column ‘Annual % ROI’. Be sure to interpret your results. School Type Private Private Private Public Private Public Private Private Private Private Private Private Private Private Private Public Public Private Private Private Best College ROI by Majo 2013: Payscale.com Cost $222,700.00 $176,400.00 $212,200.00 $125,100.00 $212,700.00 $92,910.00 $214,900.00 $217,800.00 $225,600.00 $217,300.00 $226,500.00 $215,500.00 $223,500.00 $226,600.00 $189,300.00 $89,700.00 $87,030.00 $218,200.00 $229,900.00 $148,800.00 30 Year ROI $1,786,000.00 $1,758,000.00 $1,714,000.00 $1,535,000.00 $1,529,000.00 $1,501,000.00 $1,485,000.00 $1,483,000.00 $1,444,000.00 $1,442,000.00 $1,441,000.00 $1,438,000.00 $1,428,000.00 $1,414,000.00 $1,397,000.00 $1,382,000.00 $1,376,000.00 $1,343,000.00 $1,339,000.00 $1,321,000.00 Annual ROI 7.70% 8.40% 7.80% 9.10% 7.40% 10.10% 7.30% 7.20% 7.00% 7.10% 7.00% 7.20% 7.00% 7.00% 7.50% 9.90% 10.00% 6.90% 6.70% 8.10% School Type Private Private Private Private Private Public Private Private Public Private Public Private Public Private Public Public Public Public Private Public Cost $221,700.00 $213,000.00 $230,100.00 $222,600.00 $225,800.00 $87,660.00 $224,900.00 $221,600.00 $125,100.00 $215,700.00 $92,530.00 $217,800.00 $89,700.00 $229,600.00 $101,500.00 $115,500.00 $104,500.00 $69,980.00 $219,400.00 $64,930.00 30 Year ROI Annual ROI $2,412,000.00 8.70% $2,064,000.00 8.30% $1,949,000.00 7.90% $1,947,000.00 8.00% $1,938,000.00 8.00% $1,937,000.00 11.20% $1,915,000.00 7.90% $1,878,000.00 7.90% $1,854,000.00 9.80% $1,794,000.00 7.90% $1,761,000.00 10.60% $1,752,000.00 7.70% $1,727,000.00 10.70% $1,716,000.00 7.50% $1,703,000.00 10.20% $1,694,000.00 9.70% $1,690,000.00 10.10% $1,685,000.00 11.50% $1,676,000.00 7.60% $1,668,000.00 11.70% ...
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Tutor Answer

textsformoney
School: Boston College

Thank you

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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