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14 out of 20 covid samples came back positive. find a 90% confidence interval for the...

14 out of 20 covid samples came back positive. find a 90% confidence interval for the proportion who are negative.

Math   Statistics-And-Probability   
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Answer #1

solution

Point estimate = sample proportion = = x / n = 14/20=0.7

1 -   = 0.3

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E    Z/2 * (( * (1 - )) / n)

= 1.645 *((0.7*0.73) /20 )

= 0.169

A 90% confidence interval is ,

- E < p < + E

0.7-0.169 < p < 0.7+0.169

0.531< p < 0.869

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