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Svetach [21]
3 years ago
6

Two studies were completed in California. One study in northern California involved 1,000 patients; 74% of them experienced flul

ike 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%.
Mathematics
2 answers:
Mkey [24]3 years ago
8 0
<span>The northern California study with a margin of error of 3.2%.</span>
madreJ [45]3 years ago
5 0

Answer:

<em>A.</em><em> The northern California study with a margin of error of </em><em>3.2%.</em>

Step-by-step explanation:

We know that,

\text{M.E}=Z_{critical}\cdot \sqrt{\dfrac{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.

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

Putting the values,

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

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


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