In the 2008 Olympic Men’s Marathon, 76 athletes finished the race. Their times are stored in the file Olympic Marathon. Use the times stored in the Minutes column.
(a) Use StatKey, other technology, or a random number table to randomly select 10 values. Indicate which values you’ve selected and compute the sample mean.
(b) Repeat part (a) by taking a second sample and calculating the mean. Make a mini-dotplot by plotting the two sample means on a dotplot.
(c) Find the mean for the entire population of 76 race times. Use correct notation for your answer. Comment on the accuracy of using the sample means found in parts (a) and (b) to estimate the population mean.
(d) Suppose we take many samples of size n = 10 from this population of values and plot the mean for each sample on a dotplot. Describe the shape and center of the result. Draw a rough sketch of a possible distribution for these means.