Question

300 people’s resting respiration rates are recorded, and the mean of these rates is found to be 11.4 breaths per minute (bpm).  Test the claim, at the 1% significance level, that the mean resting respiration rate is lower than the normally accepted value of 12.  Assume a population standard deviation of 2.2 bpm.  

Answer 1

Null and alternative hypotheses

Ho : = 12

H1 : < 12

Level of significance a = 0.01

Zcritical for a = 0.01 , left tailed test

Zcritical = Z​​​​​​0.01 = -2.33

Z test statistic

Z = ( xbar - )/( /√n)

Z = ( 11.4 -12)/(2.2/√300)

Z test statistic = -4.72

Decision rule : Reject the null hypothesis Ho if Z < -2.33 otherwise fail to reject the null hypothesis

Our Z = -4.72 < -2.33

Conclusion : Reject the null hypothesis , There is sufficient evidence to conclude thatthat the mean resting respiration rate is lower than the normally accepted value of 12