Atelevision sports commentator wants to estimate the proportion of citizens who "follow professional football."
(a) what sample size should be obtained if he wants to be within 2 percentage points with 94% confidence if he uses an estimate of 48% obtained from a poll? the sample size (round up to the nearest integer.)
(b) what sample size should be obtained if he wants to be within 2 percentage points with 94% confidence if he does not use any prior estimates? the sample size is (round up to the nearest integer.)

a)2206  b) 2209

Step-by-step explanation:

Formula to find the sample size :

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

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

where, 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 =

Required sample size would be :

Simply ,

 [Rounded to the next whole number.]

∴ The sample size is 2206.

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

Margin of error : E= 0.02

z-value for 94% confidence =

Required sample size would be :

Simply ,

∴ The sample size is 2209.

a. the are of the rectangle is 18.25

b. 18.25 times two is 36.50

rae me : d

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