The CDC estimates that each year in the United States, on average, 5% to 20% of the population gets the ﬂu. Using 20% as our best guess (p∗), ﬁnd how large a sample would be needed to get a ±2 percentage point margin on a 95% conﬁdence interval for the population proportion of Americans who get the ﬂu in a given year.
a. 1536
b. 1537
c. 2401
d. 2402
e. 40

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JeanaShupp JeanaShupp · Answer 1 · 2019-12-12T06:36:49+01:00

Answer: b. 1537

Step-by-step explanation:

When prior estimate of population proportion is available , then the formula for sample size: [tex]n=p(1-p)(\dfrac{z^*}{E})^2[/tex]

, where p= prior estimate of population proportion

z*= critical-value.

E= Margin of sampling error.

Let p be the proportion of population gets the ﬂu.

As per given , we have

p=20%=0.20

E= ± 0.02

Using z-table , the critical z-value corresponding to 95% confidence level = z*=1.960

Substitute all the values in the above formula , we get

Required sample size :[tex]n=(0.20)(1-0.20)(\dfrac{(1.96)}{0.02})^2[/tex]

[tex]\Rightarrow\ n=(0.20)(0.80)(98)^2[/tex]

[tex]\Rightarrow\ n=0.16(9604)\\\\\Rightarrow\ n=1536.64\approx1537[/tex] [Rounded to next integer.]

Thus, the minimum sample size needed = 1537

Hence, the correct answer = b. 1537