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A landscaping firm is interested in estimating the proportion of trees that survive one year after...

A landscaping firm is interested in estimating the proportion of trees that survive one year after being planted. Based on a cluster sample of 63 clients it is found that out of the 598 trees that were planted, 545 survived. What would be a 95% confidence interval for the true proportion of trees that survived one year?

Math   Statistics-And-Probability   
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Answer #1

We need to construct the 95% confidence interval for the population proportion. We have been provided with the following information about the number of favorable cases:

Favorable Cases X = 545
Sample Size N = 598

The sample proportion is computed as follows, based on the sample size N=598 and the number of favorable cases X=545:

The critical value for α=0.05 is . The corresponding confidence interval is computed as shown below:

Therefore, based on the data provided, the 95% confidence interval for the population proportion is 0.889<p<0.934

Let me know in comments if anything is not clear. Will reply ASAP. Please do upvote if satisfied.

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