Question

In a random sample of jails (N = 110) from the COJ, the mean number of male juveniles confined per facility was 1.17 (s = 6.21). Construct a 99% confidence interval around this sample value and interpret the interval in words.

Answer 1

The provided sample mean is 1.17 and the sample standard deviation is s = 6.21 The size of the sample is n = 110 nd the required confidence level is 99%.

The number of degrees of freedom are df = 110 - 1 = 109 , and the significance level is α=0.01.

Based on the provided information, the critical t-value for α=0.01 and df = 109 degrees of freedom is t_c = 2.622

The 99% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 99 % confidence for the population mean μ is

which completes the calculation.

there is 99% confidence that the mean value male juveniles confined will be between ( 0, 2.722 )

As male juveniles confined has lower bound 0 ( since number of people )