Question

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%.

Answer 1

Answer:a

Step-by-step explanation:test

Answer 2

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.