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Two studies were completed in California. One study in northern California involved 1,000 patients; 74% of them experienced flulike symptoms during the month of December. The other study, in southern California, involved 500 patients; 34% of them experienced flulike symptoms during the same month. Which study has the smallest margin of error for a 98% confidence interval?

The northern California study with a margin of error of 3.2%.
The southern California study with a margin of error of 3.2%.
The northern California study with a margin of error of 4.9%.
The southern California study with a margin of error of 4.9%.

2 Answers

7 votes

Answer:a

Step-by-step explanation:test

User MattMcKnight
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4 votes

Answer:

A. The northern California study with a margin of error of 3.2%.

Explanation:

We know that,


\text{M.E}=Z_(critical)\cdot \sqrt{(p(1-p))/(n)}

Where,

M.E = margin of error,


Z_(critical) = z score of the confidence interval,

for 98% confidence interval
Z_(critical)=2.33

p = proportion,

n = sample size.

One study in northern California involved 1,000 patients; 74% of them experienced flu like symptoms during the month of December.

Putting the values,


\text{M.E}=2.33\cdot \sqrt{(0.74(1-0.74))/(1000)}=0.032=3.2\%

The other study, in southern California, involved 500 patients; 34% of them experienced flu like symptoms during the same month.

Putting the values,


\text{M.E}=2.33\cdot \sqrt{(0.34(1-0.34))/(500)}=0.049=4.9\%

The smallest margin of error is 3.2% of the northern California study.


User Maged Makled
by
9.1k points
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