A researcher hypothesized that the pulse rates of long-distance athletes differ from those of other athletes. He believed that the runners’ pulses would be slower. He obtained a random sample of 10 long-distance runners. He measured their resting pulses. Their pulses were 45, 45, 64, 50, 58, 49, 47, 55, 50, 52 beats per minute. The average resting pulse of athletes in the general population is normally distributed with a pulse rate of 60 beats per minute.
Let's use 95% confidence level t-test. H0: M>=m H1:M<m At first we calculate standard deviation of a sample: sigma=sqrt(summ((xi-m)^2)/(n-1))=6.02 Now, we calculate statistic: (51.5-60)/6.02=-1.41. t-value for alpha=0.05 with 9 degrees of freedom is -1.83, so there is not enough evidence to reject H0. If we use 90% confidence level we get t-value of -1.383 so we would reject H0, so the runners' pulse would be believed to be slower.