Question

The principal at Riverside High School would like to estimate the mean length of time each day that it takes all the buses to arrive and unload the students. How large a sample is needed if the principal would like to assert with 90% confidence that the sample mean is off by, at most, 7 minutes. Assume that s = 14 minutes based on previous studies. Show all your work.

Answer 1

Answer: 11

Step-by-step explanation:

Formula to find the sample size using sample standard deviation (s) :

$n= (\dfrac{z^*\cdot s}{E})^2$ , where z* = critical z-value and E = Margin of error.

As per given , we have

E= 7

s= 14 minutes

We know that the critical value for 90% confidence interval = z*=1.645

Then, the required sample size = $n= (\dfrac{(1.645)\cdot (14)}{7})^2$

$n= (1.645\cdot 2)^2=(3.29)^2=10.8241\approx11$

Hence, the required sample size = 11