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Read the passage and answer the questions.
A study was conducted to investigate the relationship between the number of hours a student studies…
A study was conducted to investigate the relationship between the number of hours a student studies per week (X) and their scores on a standardized test (Y). The following statistical data was collected from a sample of 50 students:
The correlation coefficient between X and Y is 0.65.
| X | Y | |
|---|---|---|
| Mean | 15 | 75 |
| Standard Deviation (SD) | 4 | 10 |
(a)[2.0]
Estimate the test score for a student who studies 20 hours per week.
(b)[2.0]
If the pass mark is 40, then how many hours does a student need to study to pass?
Answer
Answer (a)
Official answer key$b_{yx} = r\frac{\sigma_y}{\sigma_x} = 0.65 \times \frac{10}{4} = 1.625$
$b_{xy} = r\frac{\sigma_x}{\sigma_y} = 0.65 \times \frac{4}{10} = 0.26$
$y - \bar{y} = b_{yx}(x - \bar{x}) \Rightarrow y - 75 = 1.625(x - 15) \Rightarrow y = 1.625x + 50.625$
$x - \bar{x} = b_{xy}(y - \bar{y}) \Rightarrow x - 15 = 0.26(y - 75) \Rightarrow x = 0.26y - 4.5$
At $x = 20$, $y = 83.125$
Final answer: 83.125
Answer (b)
Official answer keyAt $y = 40$, $x = 5.9$ hours.
From ISC 2025 Practice Mathematics, question 118.