Question

You want to find the mean number of chocolate chips in a certain brand of cookie. a) How many cookies must you randomly select for testing if you want to be 99% confident that the sample mean is within 2 chocolate chips of the population mean? (Assume a previous study found the standard deviation of chips to be 4.2)

   b) Would it be ok to sample 50 cookies? ________________Why or why not? __________

  

Answer 1

The following information is provided,
Significance Level, α = 0.01, Margin or Error, E = 2, σ = 4.2

The critical value for significance level, α = 0.01 is 2.58.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (zc *σ/E)^2
n = (2.58 * 4.2/2)^2
n = 29.35

Therefore, the sample size needed to satisfy the condition n >= 29.35 and it must be an integer number, we conclude that the minimum required sample size is n = 30
Ans : Sample size, n = 30

b)
If 50 cookies are samples
E = 2.58*4.2/sqrt(50) = 1.53
which is less than 2, hence it is okay.