A 2005 study by researchers set out to determine whether dogs could be trained t

Question

A 2005 study by researchers set out to determine whether dogs could be trained to detect lung and breast cancer by sniffing exhaled breath samples. for the breast cancer portion, breath samples from 6 cancer patients and 17 cancer-free volunteers were used. Each dog had to sniff five breath samples. 125 of the trials involved one cancer sample and 4 control samples. A correct response on these trials involved lying down next to the sample from the breast cancer patient. Collectively, the dogs correctly identified the cancer sample in 110 of these trials. Construct a 95% confidence interval for the true proportion of times these dogs will correctly identify a breast cancer sample.

Explanation / Answer

Sample proportion p = 110/125
Std deviation of measured proportion = [(110/125 * 15/125) / 125] = 0.0291
95% confidence interval = 110/125 ± 0.0291*1.96 = 0.88 ± 0.0568

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