Question

The time needed for college students to complete a certain paper-and-pencil maze follows a normal distribution with a mean of 30 seconds and a standard deviation of 2 seconds. You wish to see if the mean time μ is changed by vigorous exercise, so you have a group of 20 college students exercise vigorously for 30 minutes and then complete the maze. It takes them an average of x¯=27.2 seconds to complete the maze. Use this information to test the hypotheses H0:μ=30 Ha:μ≠30 Conduct a test using a significance level of α=0.01. (a) The test statistic (b) The positive critical value, z =

Answer 1

Solution:

a ) Given that,

= 30

= 27.2

= 2

n = 20

The test stastic z is,

z = ( -  ) /  ( /     n)

z =( 27.2 - 30 ) / ( 2 / 20 1

z = ( - 2.8 *  20 / 2 )

z = (- 2.8*20 ) / 2

z = - 6.26

Test  statistic   = -6.26

b ) This is the two tailed test .

= 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

The positive critical value, z = 2.58