A random sample of 54 students in a statistics class were asked how many hours they had studied before a statistics test.The linear model equation below describes the relationship between the mean test mark and the hours of study.mark == 4.04 ++ 0.27 ×× studyBased on this linear model, which of the following statements is correct?Choose ONE:A student who gets one more mark than another in the test is expected to have studied for 4.04 more hours.A student who did not study would be expected to get 4.04 marks in the test.A student who got zero marks in the test is expected to have studied for 4.04 hours.A student who studies 1 hour more than another is expected to get 4.04 more marks in the test.
Question
A random sample of 54 students in a statistics class were asked how many hours they had studied before a statistics test.The linear model equation below describes the relationship between the mean test mark and the hours of study.mark == 4.04 ++ 0.27 ×× studyBased on this linear model, which of the following statements is correct?Choose ONE:A student who gets one more mark than another in the test is expected to have studied for 4.04 more hours.A student who did not study would be expected to get 4.04 marks in the test.A student who got zero marks in the test is expected to have studied for 4.04 hours.A student who studies 1 hour more than another is expected to get 4.04 more marks in the test.
Solution
The correct statement is: A student who did not study would be expected to get 4.04 marks in the test.
This is because in the linear model equation, 4.04 is the y-intercept, which represents the expected value of the dependent variable (in this case, the test mark) when the independent variable (hours of study) is zero. So, if a student did not study at all (0 hours), their expected test mark would be 4.04.
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