Question- Calculate the exact 95% upper and lower confidence limits for the popu

Question

Question-

Calculate the exact 95% upper and lower confidence limits for the population proportion, which is female. Please answer using excel.

ID Sex Sex1 Age 1 F 1 46 2 F 1 87 3 F 1 70 4 M 0 72 5 F 1 82 6 F 1 85 7 F 1 73 8 M 0 65 9 M 0 73 10 F 1 94 11 F 1 94 12 M 0 79 13 M 0 82 14 F 1 76 15 M 0 72 16 F 1 91 17 F 1 90 18 F 1 83 19 F 1 82 20 F 1 49 21 F 1 88 22 F 1 75 23 M 0 81 24 F 1 76 25 F 1 85 26 F 1 84 27 F 1 77 28 F 1 94 29 F 1 66 30 M 0 72 31 M 0 78 32 F 1 86 33 F 1 70 34 M 0 72 35 M 0 91 36 M 0 75 37 F 1 83 38 M 0 82 39 F 1 82 40 F 1 92 41 F 1 79 42 F 1 69 43 F 1 76 44 M 0 73 45 F 1 83 46 F 1 80 47 F 1 76 48 F 1 77 49 F 1 85 50 F 1 70 51 M 0 81 52 F 1 83 53 M 0 76 54 F 1 88 55 M 0 88 56 F 1 89 57 M 0 39 58 F 1 89 59 M 0 80 60 F 1 71 61 F 1 90 62 M 0 91 63 F 1 73 64 F 1 77 65 F 1 78 66 F 1 79 67 F 1 85 68 F 1 74 69 M 0 78 70 F 1 92 71 M 0 56 72 M 0 76 73 F 1 84 74 F 1 75 75 F 1 68 76 M 0 50 77 M 0 49 78 M 0 76 79 M 0 76 80 F 1 67 81 M 0 96 82 F 1 83 83 F 1 77 84 M 0 86 85 F 1 80 86 F 1 61 87 M 0 80 88 F 1 78 89 F 1 71 90 M 0 90 91 F 1 91 92 F 1 69 93 M 0 88 94 F 1 76 95 F 1 83 96 F 1 75 97 M 0 83 98 M 0 68 99 M 0 75 100 M 0 60

Explanation / Answer

Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
count of femal in 100 observation is =64
Sample Size(n)=100
Sample proportion = x/n =0.64
Confidence Interval = [ 0.64 ±Z a/2 ( Sqrt ( 0.64*0.36) /100)]
= [ 0.64 - 1.96* Sqrt(0.002) , 0.64 + 1.96* Sqrt(0.002) ]
= [ 0.546,0.734]

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