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 2.2 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¯=29.8 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, z0 =
Solution :
Given that,
= 29.8
= 30
= 2.2and
n = 20
(a)
Test statistic = z = ( -
) /
/
n = (29.8 - 30) / 2.2 /
20 = -0.4066
(b)
= 0.01
/ 2 = 0.01 / 2 = 0.005
Z/2 = Z0.005 =
2.576
Critical value = 2.576
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