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

Santa Fe black-on-white is a type of pottery commonly found at archaeological excavations at a certain monument. At one excavation site a sample of 572 potsherds was found, of which 363 were identified as Santa Fe black-on-white.

(a) Let p represent the proportion of Santa Fe black-on-white potsherds at the excavation site. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 95% confidence interval for p. (Round your answers to three decimal places.)

lower limit
upper limit

Respuesta :

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

[tex]\hat{p} = \dfrac{x}{n} = \dfrac{363}{572} = 0.6346[/tex]

b) 95% confidence interval

[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]

Putting the values, we get:

[tex]0.6346\pm 1.96(\sqrt{\frac{0.6346(1-0.6346)}{572}}) = 0.6346\pm  0.0395\\\\=(0.5951,0.6741)[/tex]

Lower limit: 0.5951

Upper limit: 0.6741

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