Question

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

Answer 1

Answer:

a) p = 0.6346

b) 95% confidence interval

Lower limit: 0.5951

Upper limit: 0.6741      

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 572

Number of Santa Fe black-on-whitepots , x = 363

a) proportion of Santa Fe black-on-white potsherds

$\hat{p} = \dfrac{x}{n} = \dfrac{363}{572} = 0.6346$

b) 95% confidence interval

$\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting the values, we get:

$0.6346\pm 1.96(\sqrt{\frac{0.6346(1-0.6346)}{572}}) = 0.6346\pm 0.0395\\\\=(0.5951,0.6741)$

Lower limit: 0.5951

Upper limit: 0.6741