MATLAB: An Introduction with Applications
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Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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6. Gravetter/Wallnau/Forzano, Essentials - Chapter 8 - End-of-chapter question 9
The psychology department is gradually changing its curriculum by increasing the number of online course offerings. To evaluate the effectiveness of this change, a random sample of n = 36 students who registered for Introductory Psychology is placed in the online version of the course. At the end of the semester, all students take the same final exam. The average score for the sample is M = 76. For the general population of students taking the traditional lecture class, the final exam scores form a normal distribution with a mean of μ = 71.
If the final exam scores for the population have a standard deviation of σ = 12, does the sample provide enough evidence to conclude that the new online course is significantly different from the traditional class? Use a two-tailed test with α = .05.
z-critical | = | ±
|
z | = |
|
These results indicate:
Failure to reject the null hypothesis; the course has a significant effect
Rejection of the null hypothesis; the course does not have a significant effect
Failure to reject the null hypothesis; the course does not have a significant effect
Rejection of the null hypothesis; the course has a significant effect
If the final exam scores for the population have a standard deviation of σ = 18, does the sample provide enough evidence to conclude that the new online course is significantly different from the traditional class? Again, use a two-tailed test with α = .05. (Round z score to two decimal places.)
z-critical | = | ±
|
z | = |
|
These results indicate:
Failure to reject the null hypothesis; the course has a significant effect
Rejection of the null hypothesis; the course has a significant effect
Rejection of the null hypothesis; the course does not have a significant effect
Failure to reject the null hypothesis; the course does not have a significant effect
Comparing your answers for the two cases, explain how the magnitude of the standard deviation influences the outcome of a hypothesis test.
A smaller standard deviation produces a larger standard error, which reduces the likelihood of rejecting the null hypothesis.
A larger standard deviation produces a larger standard error, which reduces the likelihood of rejecting the null hypothesis.
A larger standard deviation produces a smaller standard error, which reduces the likelihood of rejecting the null hypothesis.
A smaller standard deviation produces a smaller standard error, which reduces the likelihood of rejecting the null hypothesis.
Expert Solution
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Step 1
Given information
Sample mean = 76
Population mean µ = 71
Sample size = 36
Standard deviation = 12
Significance level (α) = 0.05
Null and Alternative Hypothesis
Null Hypothesis: -
H0: µ = 71
Alternative Hypothesis:-
i.e. µ ≠ 71
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