Answered

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Mary is planning to survey a sample of women to find out how much money the average woman spent on lipstick last year. What sample size will she need, if she wants to be 95% confident that her sample mean is no more than $4 away from the population mean, and assuming a standard deviation of $20? A. 100

Sagot :

JeanaShupp

Answer: The required sample size = 97

Step-by-step explanation:

If prior population standard deviation is known, then the minimum sample size can be computed as:

[tex]n=(\frac{z^*\times\sigma}{E})^2[/tex]

,where z* = critical z-value

[tex]\sigma[/tex] = population standard deviation

E = Margin of error

As per given,

[tex]\sigma=20,\ E= 4[/tex]

Critical value for 95% confidence = 1.96

[tex]n=(\frac{1.96\times20}{4})^2\\= (1.96\times 5)^2\\= (9.8)^2\\=96.04\approx97[/tex]

Hence, the required sample size = 97

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