Question

I have rolled a pair of dice 60 times, I obtained a sum of 7 9 times for a proportion of .15

I need help estimating the true proportion of times that a sum of 7 occurs to within one percentage point with 95% confidence. how many rolls would be required? I need help with the steps please.  

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin of Error, E = 0.01

The provided estimate of proportion p is, p = 0.15
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 proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.15*(1 - 0.15)*(1.96/0.01)^2
n = 4898.04

Therefore, the sample size needed to satisfy the condition n >= 4898.04 and it must be an integer number, we conclude that the minimum required sample size is n = 4899
Ans : Sample size, n = 4899 or 4898