A researcher wishes to estimate, with 95% confidence, the population proportion

Question

A researcher wishes to estimate, with 95% confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate within 11% of the true 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 44%

of the respondents said they think their president can control the price of gasoline.

c) Compare the results from parts (a) and (b).

Explanation / Answer

For 95% the critical z value is 1.96

E = 11% = 0.11

Question a)

n = (zc / E)^2*p*(1-p)

Here p not given so we take as 50% (0.5)

N = (1.96/0.11)^2*0.5*(1-0.5)

   = (1.96/0.11)^2*0.5*0.5

= 79.4

~ 79

Answer: 79

Note: In few cases they consider the answer as 80

Question b)

P = 0.44

N = (1.96/0.11)^2*0.44*(1-0.44)

   = (1.96/0.11)^2*0.44*0.56

= 78.2

~ 78

Answer: 78

Note: In few cases they consider the answer as 79

Question c)

Answer: As the p-value got changes in part ( b ) we find the sample size got decreased.

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