Suppose that you are interested in determining the average height of a person in a large city. You begin by collecting the heights of a random sample of 196 people from the city. The average height of your sample is 65 inches, while the standard deviation of the heights in your sample is 3' inches. The standard error of your estimate of the average height in the city is [3.5 5 Points: Explanation: Close Explanation Statisticians use various methods of measuring the uncertainty and reliability of parameter estimates. One of these measures is the standard error of a sample mean, which is computed as the standard deviation of the sample divided by the square root of the sample size. In this case, since the standard deviation of the sample is Ir' Inches and the sample size Is 196, the standard error of your sample mean is i' = 0.5. TE H- = A. useful rule of thumb is that the true value of the parameter lies within the range of two standard errors on either side of the parameter estimate: 95 percent of the time. In this case, this means that the true average height of people in the city lies between 65 (9.. X 0.5:] and 65 + (9.. x 0.5:] inches, with 95 percent certainty. The measure of standard error can also be applied to the parameter estimates resulting from linear regressions. For example, consider the following linear regression equation that describes the relationship between education and wage: WAGE; = Bo + B EDUC; + e; where WAGE; is the hourly wage of person i (i.e., any specific person) and EDUC; is the number of years of education for that same person. The residual e; encompasses other factors that influence wage, and is assumed to be uncorrelated with education and have a mean of zero. Suppose that after collecting a cross-sectional data set, you run an OLS regression to obtain the following parameter estimates: WAGE; = -12.3 + 3.3 EDUC; If the standard error of the estimate of 81 is 1.07, then the true value of /1 lies between and . As the number of observations in a data set grows, you would expect this range to in size