Out of 200 people sampled, 116 preferred Candidate A. Based on this, estimate what proportion of the voting population prefers Candidate A with 99\% confidence.

UkusakazaL

UkusakazaL

Answered question

2021-08-10

Out of 200 people sampled, 116 preferred Candidate A. Based on this, estimate what proportion of the voting population prefers Candidate A with 99% confidence.
Out of 500 people sampled, 455 had kids.
The best point estimate for pp is.
The margin of error for a 99% confidence interval is.

Answer & Explanation

Ian Adams

Ian Adams

Skilled2021-08-16Added 163 answers

Step 1
We need to construct the 99% confidence interval for the population proportion.
Number of favorable cases x=116
Sample size n=200
The sample proportion is calculated as,
p^=xn=116200=0.58
Step 2
The critical value for significance level α=0.01 is zc=2.5758
The 99% confidence interval is computed as follows,
C.I.=(p^=zcp^(1p^)n, p^+zcp^(1p^)n)
=(0.582.57580.58(10.58)200, 0.58+2.57580.58(10.58)200)
=(0.580.0899, 0.58+0.0899)
=(0.4901, 0.6699)
Therefore, the 99% confidence interval for the population proportion is, 0.4901<p>0.6699
Which indicates that we are 99% confident that the true population proportion is contained by the intervals (0.4901, 0.6699)

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