Calculate confidence intervals at the 95% level using the Penn State football championship voting 80/20 split examples on Page 2 and use samples of 50, 500, 2000, and 5000 to see the point of diminishing returns for yourself.

1.n = 50

80 x 20=1600= 32, square root of = 5.66, rounded to 6

5050

95 % confidence level = 6 x 2 = 12

95% confidence intervals =

80+12= 68% - 92% of the population responds 'Yes'

20+12= 8% - 32% of the population responds 'No'

2.n = 500

80 x 20=1600= 3.2, square root of = 1.79, rounded to 2

500500

95 % confidence level = 2 x 2 = 4

95% confidence intervals =

80+4= 76% - 84% of the population responds 'Yes'

20+4= 16% - 24% of the population responds 'No'

3.n = 2000

80 x 20=1600= 0.8, square root of = 0.89

20002000

95 % confidence level = 0.89 x 2 = 1.78

95% confidence intervals =

80+1.78= 78.22% - 81.78% of the population responds 'Yes'

20+1.78= 18.22% - 21.78% of the population responds 'No'

4.n = 5000

80 x 20=1600= 0.32, square root of = 0.57

50005000

95 % confidence level = 0.57 x 2 = 1.14

95% confidence intervals =

80+1.14= 78.86% - 81.14% of the population responds 'Yes'

20+1.14= 18.86% - 21.14% of the population responds 'No'

Calculate confidence intervals around the P and Q percentages using the following sample data:

1. P = 75% , Q = 25% n= 678 @ 95% level of confidence

P x Q=75 x 25=1875= 2.77, square root of=1.66( rounded to 2)

N678678

2 x 2 = 4%

95% interval = 75% +/- 4%=71% - 79%

25% +/- 4%=21% - 29%

2.P = 75%, Q = 25% n= 35 @ 95% level of confidence

75 x 25=1875=53.6, square root of=7.32(rounded to 7)

3535

7 x 2 = 14%

95% interval = 75% +/- 14% =61% - 89%

25% +/- 14% =11% - 39%

3.P = 52%, Q = 48% n= 678 @ 99% level of confidence

52 x 48=2496=3.68, square root of=1.92(rounded to 2)

678678

2 x 3 = 6%

99% interval = 52% +/- 6% = 46% - 58%

48% +/- 6% = 42% - 54%

Why would rounding the figures to the integer for the first two questions, and then to the nearest hundredths for the next two? Please give a justification. I'm having a hard time understanding this.