Question

1. A recent study from Great Britain examined the relationship between the number of friends an individual has on Facebook and grey matter density in the areas of the brain associated with social perception and associative memory. Forty students from City University London participated in this study. We will examine the grey matter density. The value of grey matter density is reported as a z-score.

A) Interpret the interval in the context of the problem. (95 percent confidence interval: -0.4076953 , 0.2076953)

Answer 1

A confidence interval for mean is a way of expressing the uncertainty in x as an estimate of μ. A 95% confidence interval means we are 95% confidence that the interval contains the true population mean.

In this case, (95 percent confidence interval: -0.4076953 , 0.2076953) means we are 95% confident that the true mean grey matter density falls in the calculated interval. In other words, if we collect data this way many times, 95 times out of 100, the mean of the data set of grey matter densities will fall in the above range.