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xz_007 [3.2K]
3 years ago
14

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:
kramer3 years ago
7 0

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

Step-by-step explanation:

The formula for margin of error for proportion is given by :-

z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}

Given : Significance level : \alpha:1-0.98=0.02

Critical value : z_{\alpha/2}=2.33

For northern California , the sample size was takes : n= 1000

The proportion of patients  experienced flu like symptoms during the month of December = 0.74

Then , the margin of error will be :-

(2.33)\sqrt{\dfrac{0.74(1-0.74)}{1000}}\approx0.032=3.2\%

For southern California , the sample size was takes : n= 500

The proportion of patients  experienced flu like symptoms during the month of December = 0.34

Then , the margin of error will be :-

(2.33)\sqrt{\dfrac{0.34(1-0.34)}{500}}\approx0.049=4.9\%

Clearly, the northern California study with a margin of error of 3.2%  has the smallest margin of error for a 98% confidence interval.

gtnhenbr [62]3 years ago
4 0
The  study has the smallest margin of error for a 98% confidence interval is <span>The northern California study with a margin of error of 3.2%.

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
</span>
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