Question

show the work plz

An astronomer is interested in measuring in light years, the distance from his observatory to a distant star. If the astronomer believes that the values of the measurements are independent and identically distributed random variables with common mean d (the actual distance) and a common variance of 9 (light years), how many measurements must he make to be 99% sure that his estimated distance is accurate to within + - 1.0 light year? (Note: for 95% confidence, Phi(Z) >= 0.975, which means that Z = 1.96) (Note: for 99 % confidence, Phi(Z) >=0.995, which means that Z = 2.575)

Answer 1

The following information is provided,
Significance Level, α = 0.01, Margin or Error, E = 1, σ = 3

The critical value for significance level, α = 0.01 is 2.576.

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 = (2.575 * 3/1)^2
n = 59.67

Therefore, the sample size needed to satisfy the condition n >= 59.72 and it must be an integer number, we conclude that the minimum required sample size is n = 60
Ans : Sample size, n = 60