Question

For the data below construct a 95% confidence interval for the population mean.53.4 51.6 48.0 49.8 52.8 51.8 48.8 43.4 48.2 51.8 54.6 53.8 54.6 49.6 47.2

Answer 1

The 95% confidence interval is given below:

`\bar{x} \pm t_{(0.05)/(2)} \left( (s)/(√(n)) \right)`

Where:

`\bar{x} = 50.63` is the sample mean

`t_{(0.05)/(2) } =2.145` is the critical value at 0.05 significance level for df = n-1 = 15 - 1 =14

`s=3.1576` is the sample standard deviation

`\therefore 50.63 \pm 2.145 \left( (3.1576)/(√(15)) \right)`

`50.63 \pm 1.75`

`\left(50.63 - 1.75, 50.63+1.75 \right)`

`\left(48.88,52.38\right)`

Therefore, the 95% confidence interval for the population mean is (48.88, 52.38)