jaretktm9920 jaretktm9920

07-02-2024
Mathematics

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For small sample sizes, an alternate method of constructing a confidence interval is available. To implement this method, first, include an additional 4 observations in the sample, 2 of which are successes and 2 of which are failures. Second, calculate a new sample proportion pˆnew for the new sample. Finally, construct a confidence interval using pˆnew , with the formula pˆnew±1. 96√pˆnew(1−pˆnew)/n+4.
For the cell phone batteries, consider a sample of 5 in which 1 battery fails to last through 500 charges. Using the alternate method described, what is the value of pˆnew ?

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