Answer :
Final answer:
A statistical significance test shows that the data collected, that seniors study for an average of 13 hours when the assumed average was 14 hours, is not statistically significant in both scenarios, whether the researchers expected any difference or a decrease. The difference or lack thereof could be driven by factors such as student study habits, course difficulty, and teaching methods.
Explanation:
The subject researchers are concern about is whether the difference in study hours is significant or not. This is a question of statistical significance and can be answered by conducting a hypothesis test with the help of Z-test or T-test.
a) Researchers conduct a study looking at the amount of time spent studying. If they are looking for any difference, the null hypothesis would state that the mean study time is equal to 14 hours. A sample mean of 13 hours with a sample size of 64 and a standard deviation of 4.8 gives a Z score of approximately -1.33 from the Z test formula , where Z = (X - μ)/(σ/√n). The two-tailed P-value corresponding to this Z score is about 0.1844, which is greater than the standard significance level of 0.05. Hence the data is not statistically significant.
b) If researchers were expecting students to study less, they are looking for a decreased mean. This situates the analysis in the context of a one-tailed test (lower). The P-value corresponding to the Z score in one-tailed test is approximately 0.0922 which is still greater than 0.05, meaning the data is insignificant.
c) The difference or lack of difference can be driven by many factors including the study habits of the students, the difficulty level of the courses, or changes in teaching methods. The number and diversity of these unknown influences are one reason why there is always some level of uncertainty attached to statistical findings.
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