Aresearcher wishes to estimate, with 95% confidence, the population proportion of adults who say chocolate is their favorite ice cream flavor. her estimate must be accurate within 4% of the population proportion.
(a) no preliminary estimate is available. find the minimum sample size needed.
(b) find the minimum sample size needed, using a prior study that found that 38% of the respondents said their favorite flavor of ice cream is chocolate.
(c) compare the results from parts (a) and (b).

a) If no preliminary estimate is available, the minimum sample size needed is 601

b) If 38% of the respondents said their favorite flavor of ice cream is chocolate in a prior survey, then the minimum sample size needed is 566

c) As the proportion estimate gets smaller, minimum sample size needed decreases.

Step-by-step explanation:

The following formula is used to compute the minimum sample size required to estimate the population proportion of adults who say chocolate is their favorite ice cream flavor within the margin of error 4%:

n≥ p×(1-p) × where

(a) When p is not known p is assumed 0.5. Then

n≥ 0.5×0.5× =600.25

(b) if p=0.38 (38%) then

n≥ 0.38×0.62× =565.68

c. (3,2,6) is the answer.

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

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