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cestrela7 [59]
3 years ago
8

A television sports commentator wants to estimate the proportion of citizens who​ "follow professional​ football." ​

Mathematics
1 answer:
Angelina_Jolie [31]3 years ago
8 0

Answer: a)2206  b) 2209

Step-by-step explanation:

Formula to find the sample size :

a) If prior population proportion (p) is known.

n=p(1-p)(\dfrac{z_{c}}{E})^2

b) If prior population proportion (p) is unknown.

n=0.25(\dfrac{z_{c}}{E})^2

where, {z_{c} is the z-value associated with confidence level and E would be the margin of error .

Solution : Let p be the proportion of citizens who​ "follow professional​ football."

a) Given : p=0.48

Margin of error : E= 0.02

z-value for 94% confidence = z_c=1.88

Required sample size would be :

n=p(1-p)(\dfrac{z_{c}}{E})^2

\Rightarrow\ n=0.48(1-0.48)(\dfrac{1.88}{0.02})^2

Simply ,

n=2205.4656\approx2206  [Rounded to the next whole number.]

∴ The sample size is <u>2206</u>.

b) Proportion of citizens who​ "follow professional​ football" is unknown.

Margin of error : E= 0.02

z-value for 94% confidence = z_c=1.88

Required sample size would be :

n=0.25(\dfrac{z_{c}}{E})^2

\Rightarrow\ n=0.25(\dfrac{1.88}{0.02})^2

Simply ,

n=2209  

∴ The sample size is <u>2209</u>.

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