Question 1091475
the random sample is > 30 so we can use a normal distribution
:
alpha = 0.05
:
Note that mu is the population mean
:
Ho:  population mean = 69 inches
Ha:  population mean is not = 69 inches
:
Ha implies a two-tailed hypothesis test
:
the standard error(SE) is s/square root(n) = 4/square root(36) = 0.6666 approx 0.67
:
the test statistic z = (67.5 - 69) / 0.67 = -2.238
:
because this is a two-tailed test we divide alpha by 2, 0.05/2 = 0.025 and the associated z-value is 1.96 and -1.96
:
*************************************
we reject Ho because -2.238 < -1.96
*************************************
: