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 2.2 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 =

Answer #1

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} = Z_{0.005} =
2.576

Critical value = 2.576

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