CheemnCatelvew

2021-08-20

The mean time to sell a residential property in the area is 60 days. You select a random sample of 20 homes sold in the last year and find the mean selling time is 65 days with a standard deviation of 9 days. Based on the data, develop a 95 percent confidence interval for the population mean.

### Answer & Explanation

Macsen Nixon

We want to construct a 95 percent confidence interval for the population mean. Confidence Interval Estimates for the Mean: If the population standard deviation is unknown and sample size is less than 30 then we use t-distribution and the confidence interval becomes $\stackrel{―}{X}±t\frac{8}{\sqrt{n}}$ Using the above formula the 95 percent confidence interval for the population mean is $\stackrel{―}{X}±{t}_{\frac{\alpha }{2},n-1}\frac{s}{\sqrt{n}}=\stackrel{―}{X}±t\left(\frac{0.05}{2.20}-1\right)\frac{s}{\sqrt{n}}$

$=65±{t}_{0.025},19\frac{9}{\sqrt{20}}$[Using t-distribution table]

$=65±4.212$
=(60.788,69.212) Therefore, the 95 percent confidence interval for the population mean is (60.788, 69.212). hence, the final answer is : The 95% confidence interval is (60.788,69.212).

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