Question

A researcher would like to determine whether caffeine has an effect on mental alertness after sleep deprivation. A sample of n = 25 participants is obtained, and each person is given a cup of coffee, after one night of total sleep deprivation, one hour before being tested in a driving simulation task. For the general population with one night of losing sleep, scores on the simulation task are normally distributed with μ = 66. The individuals in the sample had an average score of M = 58 and s = 7.

Can the researcher conclude that scores on the sleep deprivation driving simulation task are significantly different after consuming caffeine? Use α = .05. Include df, critical values used, computed statistic, and a written (verbal) response to the question above. Also include a formal write-up of the results.

(Note: Type out the answers as best you can. You may spell out the notation if you need to (e.g. mu for μ). )

Answer 1

From the given information,

M=58,s=7,mu=66,n=25

By using calculator,

df= n-1=25-1=24

Critical values= -2.0639 and 2.0639

Test statistic= (M-mu)/(s/squareroot(n))

Test statistic= (58-66)/(7/squareroot (25))

Test statistic= -5.7143

Now,

Test statistic < critical value (-2.0639)

Hence, Reject the null hypothesis at 5% level of significance.

Mu≠66

Conclusion:-

Scores on the sleep deprivation driving simulation task are significantly different after consuming caffeine.

Thank you.