Question

A toy manufacturer wants to know how many new toys children buy
each year. Assume a previous study found the
**variance** to be 3.61. She thinks the mean is 9.3
toys per year. What is the minimum sample size required to ensure
that the estimate has an error of at most 0.12 at the 90% level of
confidence? **Round your answer up to the next
integer.**

Answer #1

Solution :

Given that,

standard deviation = =3.61=1.9

Margin of error = E = 0.12

At 90% confidence level

= 1 - 90%

= 1 - 0.90 =0.10

/2
= 0.05

Z/2
= Z0.05 = 1.645 ( Using z table ( see the 0.05 value in standard
normal (z) table corresponding z value is 1.645 )

sample size = n = [Z/2* / E] 2

n = ( 1.645 *1.9 / 0.12 )2

n =678.38

Sample size = n =678

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