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Ivenika [448]
3 years ago
13

Use the normal distribution to find a confidence interval for a proportion p given the relevant sample results. Give the best po

int estimate for p, the margin of error, and the confidence interval. Assume the results come from a random sample. A 90% confidence interval for p given that p Overscript ^ EndScripts equals 0.7 and n equals 110.
Mathematics
1 answer:
Brrunno [24]3 years ago
5 0

Answer: (0.63, 7.07)

Step-by-step explanation:

The confidence interval for population proportion is given by :-

\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

Given :\hat{p} =0.7 ;  n=110

Significance level : 1-0.90=0.1

Critical value :  z_{\alpha/2}=1.645

Now, a 90% confidence interval for population proportion will be :-

0.7\pm (1.645)\sqrt{\dfrac{0.7(1-0.7)}{110}}\\\\\approx0.7\pm0.07\\\\=(0.7-0.07,0.7+0.07)=(0.63,\ 7.07)

Hence, a 90% confidence interval for population proportion = (0.63, 7.07)

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