Question

You want to construct a confidence interval for the mean number of taste buds in top chefs. Assume the population standard deviation is 900.

(a) Calculate the minimum required sample size if you want a margin of error no greater than 300 at the 95% confidence level.  

The minimum sample size is ___ chefs.

(b) What will cause the minimum required sample size to increase?

increasing the confidence level

increasing the acceptable margin of error

decreasing the acceptable margin of error

decreasing the confidence level

Answer 1

b)

The following information is provided,
Significance Level, α = 0.05, Margin or Error, E = 300, σ = 900

The critical value for significance level, α = 0.05 is 1.96.

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 = (1.96 * 900/300)^2
n = 34.57

Therefore, the sample size needed to satisfy the condition n >= 34.57 and it must be an integer number, we conclude that the minimum required sample size is n = 35
Ans : Sample size, n = 35

b)
increasing the confidence level
decreasing the acceptable margin of error