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# Testing the Different Performance of Students with and without Sleep

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a. Research has shown that losing a few hours of sleep can have a significant effect on performance of some simple tasks. To demonstrate this phenomenon, a sample of n = 25 college students was given a simple problem solving task at noon one day and again at noon on the following day. The students were not permitted any sleep a full night between the two tests. For each student, the difference between the first and second score was recorded. For this sample, the students averaged Md = 4.7 better on the first test with a variance of 64 for the difference of scores.

b. Do the data indicate a significant change in problem solving ability? Use a two tailed test with ?=.01. Be sure to show all formulas, steps, processes and calculations for all parts of the

https://brainmass.com/statistics/hypothesis-testing/testing-different-performance-students-without-sleep-507348

#### Solution Preview

Hypothesis: Ho: mud is 0 vs. Ha: mud is not 0 where mud is the true mean differnce of the first and second ...

#### Solution Summary

This solution shows how to calculate the test statistic and the critical value and interpret the results. The expert determines if the data indicates a significant change in problem solving abilities.

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## A manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is equal to \$75.

Please provide a brief explanation if possible of how to arrive at these answers.
Please see attached file for full problem description.

1. Suppose we wish to test H0: 47 versus H1: > 47. What will result if we conclude that the mean is greater than 47 when its true value is really 52?
a) We have made a Type I error.
b) We have made a Type II error.
c) We have made a correct decision.
d) None of the above is correct.

2. How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 41 Kleenex users yielded the following data on the number of tissues used during a cold: = 52, s = 22. Suppose the alternative we wanted to test was .

a) State the correct rejection region for = 0.05.
a) Reject H0 if z > 1.96
b) Reject H0 if z < - 1.64.
c) Reject H0 if t > 2.021 or t < - 2.021
d) Reject H0 if t < - 1.684.

b) Would you reject the null hypothesis?

3. A manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is equal to \$75. An auditor selects a random sample of 100 accounts and finds that the average owed is \$83.40 with a sample standard deviation of \$23.65. If you wanted to test whether the average balance is different from \$75 and decided to reject the null hypothesis, what conclusion could you draw?
a) We can conclude that the average balance is \$75.
b) We cannot conclude that the average balance is \$75.
c) We can conclude that the average balance is less than \$75.
d) Neither of the above.

4. True or False: A researcher is curious about the effect of sleep on students' test performances. He chooses 60 students and gives each 2 tests: one given after 2 hours' sleep and one after 8 hours' sleep. The test the researcher should use would be a test for dependent samples.

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