Including Probability distributions, discrete and continuous, binomial distribut
ID: 3259915 • Letter: I
Question
Including Probability distributions, discrete and continuous, binomial distribution, normal distribution, sampling distributions. Central Limit Theorem, Normal approximation to the Binomial, Estimation 54% of the grade. Three-circle, red-on-white is one distinctive pattern on ceramic vessels of the period found at an archaeological site. At one excavation, a sample of 16.1 indicated that 74 were of the three-circle, pattern. (a) Find a point estimate for the proportion of all ceramic potsherds at this site that are of the three-circle, red-on-white pattern. (Round your answer to four decimal places.) (b) Compute a 95% confidence interval for the population proportion p of all ceramic with this distractive patterns found at the site.Explanation / Answer
Here we have given that,
x = 74
n = 161
The point estimate of population proportion is p^.
p^ = x/n = 74/161= 0.4596
Now we have to find 95% confidence interval for proportion.
95% confidence interval for p is,
p^ - E < p < p^ + E
where p^ is sample proportion.
E is margin of error.
E we can find by using formula,
E= Zc * sqrt[(p*q)/n]
where q = 1-p
Zc is critical value for normal distribution.
Zc we can find by using EXCEL.
syntax :
=NORMSINV(probability)
where probability = 1 - alpha/2
where alpha = 1 - C
C = confidence level = 95% = 0.95
Zc = 1.96
E = 1.96*sqrt[(0.4596*0.5404)/161] = 0.0770
lower limit = p^ - E = 0.4596-0.0770 = 0.383
upper limit = p^ + E = 0.4596+0.0770 = 0.537
95% confidence interval for population proportion is (0.383, 0.537).
We are 95% confident that the population proportion is lies between 0.383 and 0.537.