Question

In: Statistics and Probability

The U.S. Food and Drug Administration (FDA) recently approved the marketing of a new chemical solution,...

The U.S. Food and Drug Administration (FDA) recently approved the marketing of a new chemical solution, Caridex, which disolves cavities. In a study conducted by dental researchers at Northwestern University, 21 of the 35 patients with cavities preffered treatment with Caridex to drilling (Gainesville Sun, Feb. 11, 1988). Find a 90% confidence interval for the true proportion of dental patients who prefer having cavities dissolved with Caridex rather than drilled.

(0.46,0.74)
(0.44,0.76)
(0.39,0.81)

Solutions

Expert Solution

Solution :

Given that,

n = 35

x = 21

= x / n = 21 / 35 = 0.60

1 - = 1 - 0.60 = 0.40

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

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

= 1.645 * (((0.60 * 0.40) / 35)

= 0.14

A 90% confidence interval for population proportion p is ,

- E < P < + E

0.60 - 0.14 < p < 0.60 + 0.14

0.46 < p < 0.74

(0.46 , 0.74)

orchestra answered 1 year ago
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