What is the relationship between the amount of time statistics students study per week and their final exam scores? The results of the survey are shown below.

Question

What is the relationship between the amount of time statistics students study per week and their final exam scores? The results of the survey are shown below.

Time	6	13	1	14	12	7	0
Score	55	87	56	84	87	62	51

1. Find the correlation coefficient:  Incorrect   Round to 2 decimal places.
2. The null and alternative hypotheses for correlation are:
3.  ? r μ ρ Correct  0 
4.  ? μ r ρ Correct   0  
5. The p-value is:  ___ (Round to four decimal places) 
6. Use a level of significance of  to state the conclusion of the hypothesis test in the context of the study.
7. There is statistically significant evidence to conclude that there is a correlation between the time spent studying and the score on the final exam. Thus, the regression line is useful.
8. There is statistically insignificant evidence to conclude that there is a correlation between the time spent studying and the score on the final exam. Thus, the use of the regression line is not appropriate.
9. There is statistically significant evidence to conclude that a student who spends more time studying will score higher on the final exam than a student who spends less time studying.
10. There is statistically insignificant evidence to conclude that a student who spends more time studying will score higher on the final exam than a student who spends less time studying.

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1. r^2  = __ (Round to two decimal places) 
2.  Interpret r^2 : 
3. Given any group that spends a fixed amount of time studying per week, 87% of all of those students will receive the predicted score on the final exam.
4. There is a large variation in the final exam scores that students receive, but if you only look at students who spend a fixed amount of time studying per week, this variation on average is reduced by 87%.
5. 87% of all students will receive the average score on the final exam.
6. There is a 87% chance that the regression line will be a good predictor for the final exam score based on the time spent studying.

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1. The equation of the linear regression line is:  
2. y^ =  +  x  (Please show your answers to two decimal places)  
3. Use the model to predict the final exam score for a student who spends 7 hours per week studying.
4. Final exam score = ___ (Please round your answer to the nearest whole number.)  
5. Interpret the slope of the regression line in the context of the question: 
6. For every additional hour per week students spend studying, they tend to score on averge 2.69 higher on the final exam.
7. The slope has no practical meaning since you cannot predict what any individual student will score on the final.
8. As x goes up, y goes up.

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1. Interpret the y-intercept in the context of the question: 
2. The y-intercept has no practical meaning for this study.
3. The best prediction for a student who doesn't study at all is that the student will score 48 on the final exam.
4. The average final exam score is predicted to be 48.
5. If a student does not study at all, then that student will score 48 on the final exam.

Answer 1

Hi Anni,

Question Set #1

1. Enter time and score into separate lists in a TI-83 Plus or calculator. Ex. L₁ = (6, 13, 1....) L₂ = 55, 87, 56.... Correlation coefficient is cumbersome to compute by hand. Then go to STAT-CALC-LinReg ax + b-Enter L₁, L_2. This will give you the correlation coefficient r. It will also give r², which you are asked for below.
2. Remember, null hypothesis means nothing, and you were not asked about specific direction (+ or -) of relationship so in this case:

H₀ :rho =0

H_A: rho not equal to 0

5. To get p-value, go back to the TI-83 or greater, go to STAT-TESTS-LinRegTTest. It should default to L₁ and L₂. Now, make sure the option "not equal to 0" is highlighted. Then hit "calculate." This will give you the t-test statistic and p-value.

#6. This answer depends on your p-value. If below 0.05, there is statistically significant evidence to conclude correlation, which would indicate choice a. If not, there is not, which indicates choice b. We cannot draw any conclusions about individual students, only about the collective.

Question Set #2

#1. This is the same procedure as step 1 above, only record r² instead of r. TI-83 Plus will display both. Alternatively, r² is exactly what it sounds like, so you could just multiply the correlation coefficient r by itself.

#2. Go to STAT-CALC-LinReg (ax + b). This will give you the regression line equation: y^ = 2.69x + 48.47

#3 and #4 Just plug 7 in for x in the regression line equation:

y^= 2.69(7) + 48.47

I will leave that computation to you.

#5. Slope of a regression line means that for every one unit increase in x, y^ increases (or decreases, if negative) by the slope. Since you now know what the slope means, you can pick a choice based on that.

#6. y-intercept always means that x is set equal to 0. In this case, that means a student did not study at all i.e. 0 hours. Remember that y^ always implies a prediction. Now that you know what y-intercept means, you can pick an answer choice based on it.

I hope this helps.