# Answer to Question #1553 in Statistics and Probability for Misty Cooke

Question #1553

& 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.

Expert's answer

a. t-test must be used , due to unknown variance.

b. This is a one tailed test.

c. H0: m<60;

& & Ha: m>=60

d. Tcv=-1.833 (n=10-1=9, with 0.95 confidence level )

e.

Mn=51.5

M=60, Sn=6.023

Tobt=sqrt(n)(Mn-M)/Sn=-4.462

f.Yes, we accept the hypothesis, because tobt<tcv. And the conslusion is that runners’ pulses would be slower than of other athletes.

b. This is a one tailed test.

c. H0: m<60;

& & Ha: m>=60

d. Tcv=-1.833 (n=10-1=9, with 0.95 confidence level )

e.

Mn=51.5

M=60, Sn=6.023

Tobt=sqrt(n)(Mn-M)/Sn=-4.462

f.Yes, we accept the hypothesis, because tobt<tcv. And the conslusion is that runners’ pulses would be slower than of other athletes.

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