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What is the minimal sample size needed for a 95% confidence interval to have a maximal...

What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1 in the following scenarios? (For each answer, enter a number. Round your answers up the nearest whole number.)

(a)

a preliminary estimate for p is 0.23

(b)

there is no preliminary estimate for p

Homework Answers

Answer #1

Solution :-

Given that,

a) = 0.23

1 - = 1-0.23 = 0.77

margin of error = E = 0.1

Z/2 = 1.96

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.96/0.1)2 * 0.23*0.77

= 68

sample size = n = 68

b)

= 0.50

1 - = 1-0.50 = 0.50

margin of error = E = 0.1

Z/2 = 1.96

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.96/0.1)2 * 0.50*0.50

  = 96

sample size = n = 96

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