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navik [9.2K]
3 years ago
15

web based software company is interested in estimating the proportion of individuals who use the Firefox browser. In a sample of

200 of individuals, 30 users stated that they used Firefox. Using this data, construct a 99% confidence interval for the proportion of all individuals that use Firefox. What is the lower limit on the 99% confidence interval? Give your answer to three decimal places.
Mathematics
1 answer:
nata0808 [166]3 years ago
6 0
<h2>Answer with explanation:</h2>

Let \hat{p} denotes the sample proportion.

As per given , we have

n= 200

\hat{p}=\dfrac{30}{200}=0.15

Critical value for 99% confidence : z_{\alpha/2}=2.576

Confidence interval for population proportion :-

\hat{p}\pm z_{\alpha/2} \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.15\pm (2.576)(\sqrt{\dfrac{0.15(1-0.15)}{200}})\\\\\approx0.15\pm0.065\\\\=(0.15-0.065,\ 0.15+0.065)\\\\=(0.085,\ 0.215)

Hence, a 99% confidence interval for the proportion of all individuals that use Firefox: (0.085,\ 0.215)

The lower limit on the 99% confidence interval = 0.085

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