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 * (
= 0.14
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)
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