Question

The Federal Election Commission collects information about campaign contributions and disbursements for candidates and political committees each election cycle. During the 2012 campaign season, there were 1,619 candidates for the House of Representatives across the United States who received contributions from individuals. The table below shows the total receipts from individuals for a random selection of 40 House candidates rounded to the nearest $100. $3,600 $1,243,900 $10,900 $385,200 $581,500 $7,400 $2,900 $400 $3,714,500 $632,500 $391,000 $467,400 $5,800 $56,800 $405,200 $733,200 8,000 $468,700 $75,200 $41,000 $13,300$9,500 $953,800 $1,113,500$1,109,300 $88,600 $353,900 $986,100 $378,200 $13,200 $745,100 $5,800 $3,800 $3,072,100 $1,626,700 $202,400 $512,900 $2,309,200 $6,600 $15,800 Pulled From OpenStax Statistics

Answer 1

1)

Sample Mean,    x̅ = ΣX/n =    568872.5

sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   839649.16

2)

point estimate=568872.50

3) option D)

answer: 200*5% = 10

5)

Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   39          
't value='   tα/2=   2.0227   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   839649.1557   / √   40   =   132760.1884
margin of error , E=t*SE =   2.0227   *   132760.1884   =   268532.8276
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    568872.50   -   268532.827552   =   300339.6724
Interval Upper Limit = x̅ + E =    568872.50   -   268532.827552   =   837405.3276
95%   confidence interval is (   300340 < µ <   837405 )

6)

margin of error , E=t*SE =   2.0227   *   132760.1884   =   268532.83

7) 568872.50 ± 268532.83