Question

Suppose we think that listening to classical music will affect the amount of time it takes a person to fall asleep; we conduct a study to test this idea. Answer all of the following questions:

Assume that the amount of time it takes people in the population to fall asleep is normally distributed. In the study, we have a sample of people listen to classical music and then we measure how long it takes them to fall asleep. Supposed the sample of 36 people fall asleep in 12 minutes. What is the probability of obtaining a sample mean of 12 minutes or smaller? Assuming alpha equals 0.05, is your calculated p value in the critical region? (Hint: Remember to consider two critical regions.)

Answer 1

Solution:

Assume that the amount of time it takes people in the population to fall asleep is normally distributed.

Sample Size =n = 36

Sample Mean =

Find the probability of obtaining a sample mean of 12 minutes or smaller.

Look in z table for z = -3.0 and 0.00 and find corresponding area.

P( Z < -3.00 ) = 0.0013

That is: p-value = 0.0013

Level of significance =

Since p-value = 0.0013 < 0.05 level of significance,  calculated p value is in the critical region.

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