Question

An entomologist wishes to estimate the average development time of the citrus red mite, a small spider-like insect that causes damage to leaves and fruit, correct to within 0.3 day. From previous experiments it is known that σ is approximately 6 days. What minimum sample should the entomologist take to be 95% confident of her estimate? (Round your answer up to the nearest whole number.)

n ≥  mites

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin or Error, E = 0.3, σ = 6

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 * 6/0.3)^2
n = 1536.64

Therefore, the sample size needed to satisfy the condition n >= 1536.64 and it must be an integer number, we conclude that the minimum required sample size is n = 1537
Ans : Sample size, n = 1537