Suppose you take a random sample of 64 adults, administer a driver safety test and obtain the following results:

Assume you know nothing about the population mean or distribution characteristics of driver safety scores. Calculate the standard error for this sample. Create a 95.5% confidence interval (that is 2 standard errors, note that the 95% we’ve worked with is actually 1.96 standard errors) for the mean score of the population. Interpret this confidence interval. What theorem forms the theoretical basis of the confidence interval you generated? (3%)

Solution: The standard error is defined as

The 95.5% confidence interval is given by

where, which means that

The theoretical basis for the construction of confidence intervals is the Central Limit Theorem.