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 1 8 2 4 3 3 15 Score 62 92 65 63 70 76 100 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: H0: ? = 0 H1: ? ? 0 The p-value is: (Round to four decimal places) c. Use a level of significance of ?? = 0.05 to state the conclusion of the hypothesis test in the context of the study. 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. 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. 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. 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. d. r² = (Round to two decimal places) e. Interpret r² : 84% of all students will receive the average score on the final exam. 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 84%. Given any group that spends a fixed amount of time studying per week, 84% of all of those students will receive the predicted score on the final exam. There is a 84% chance that the regression line will be a good predictor for the final exam score based on the time spent studying. f. The equation of the linear regression line is: ? = + x (Please show your answers to two decimal places) g. Use the model to predict the final exam score for a student who spends 6 hours per week studying. Final exam score = (Please round your answer to the nearest whole number.) h. Interpret the slope of the regression line in the context of the question: For every additional hour per week students spend studying, they tend to score on averge 2.82 higher on the final exam. As x goes up, y goes up. The slope has no practical meaning since you cannot predict what any individual student will score on the final. i. Interpret the y-intercept in the context of the question: The average final exam score is predicted to be 61.

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 1 8 2 4 3 3 15
Score 62 92 65 63 70 76 100
a. Find the correlation coefficient: r = Round to 2 decimal places.
b. The null and alternative hypotheses for correlation are:
H0: ? = 0
H1: ? ? 0
The p-value is: (Round to four decimal places)
c. Use a level of significance of ?? = 0.05 to state the conclusion of the hypothesis test in the context of the study.
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.
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.
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.
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.
d. r² = (Round to two decimal places)
e. Interpret r² :
84% of all students will receive the average score on the final exam.
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 84%.
Given any group that spends a fixed amount of time studying per week, 84% of all of those students will receive the predicted score on the final exam.
There is a 84% chance that the regression line will be a good predictor for the final exam score based on the time spent studying.
f. The equation of the linear regression line is:
? = + x (Please show your answers to two decimal places)
g. Use the model to predict the final exam score for a student who spends 6 hours per week studying.
Final exam score = (Please round your answer to the nearest whole number.)
h. Interpret the slope of the regression line in the context of the question:
For every additional hour per week students spend studying, they tend to score on averge 2.82 higher on the final exam.
As x goes up, y goes up.
The slope has no practical meaning since you cannot predict what any individual student will score on the final.
i. Interpret the y-intercept in the context of the question:
The average final exam score is predicted to be 61.

Added by April J.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Ariana Nash

08/16/2022

Step 1

Find the correlation coefficient: To find the correlation coefficient, we need to use the given data for time and score. However, the data is not provided in the question. Please provide the data for time and score so that we can calculate the correlation Show more…

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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 1 8 2 4 3 3 15 Score 62 92 65 63 70 76 100 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: H0: ? = 0 H1: ? ≠ 0 The p-value is: (Round to four decimal places) c. Use a level of significance of ̑̑ = 0.05 to state the conclusion of the hypothesis test in the context of the study. 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. 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. 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. 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. d. r² = (Round to two decimal places) e. Interpret r² : 84% of all students will receive the average score on the final exam. 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 84%. Given any group that spends a fixed amount of time studying per week, 84% of all of those students will receive the predicted score on the final exam. There is a 84% chance that the regression line will be a good predictor for the final exam score based on the time spent studying. f. The equation of the linear regression line is: ŷ = + x (Please show your answers to two decimal places) g. Use the model to predict the final exam score for a student who spends 6 hours per week studying. Final exam score = (Please round your answer to the nearest whole number.) h. Interpret the slope of the regression line in the context of the question: For every additional hour per week students spend studying, they tend to score on averge 2.82 higher on the final exam. As x goes up, y goes up. The slope has no practical meaning since you cannot predict what any individual student will score on the final. i. Interpret the y-intercept in the context of the question: The average final exam score is predicted to be 61.

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00:01 Okay, so in order to do this problem, the first thing i did was i took the x variable, which is time, and i put all those values into a list in my calculator by going stat, then edits, then putting in the numbers.

00:12 And i put the score into another list, okay? then in order to do all the other questions, i'll need to have some data, some analysis done.

00:25 So i go on my calculator to stat and over to tests and down to linear regression t test.

00:35 Okay.

00:38 And in this case, i am going to have the following information.

00:50 So it tells me a few different things.

00:51 First of all, when i run that t test, it gives me some output from my data.

00:57 Okay? so the first one thing that gives me that i need is the correlation coefficient r, right? and the r that it splits out, which is positive here is 0 .916.

01:11 So i guess they want us to round that to 0 .92, which is pretty high.

01:15 The null and alternative hypothesis for the correlation, if we're doing it on the correlation and not on the slope, then we're going to have a row for our, for our, for our, parameter here, okay, so that looks like an r or p, but it's really a greek r, okay, it's row.

01:36 And our alternate, or our null hypothesis is going to be that row is equal to zero, so that there's no linear relationship, and our alternative hypothesis is going to be that row is not equal to zero, or that there is a linear relationship between the two.

01:51 Okay? now, in order to find the correct conclusion we need the p value right and the p value that i see in my output when i when i look at it is 0 .0037 is what it gives me for my p value that is a low p value right so that is statistically significant so we are going to reject the null hypothesis here and say that there is a linear relationship.

02:31 There is a correlation, so i can use the regression line, and it is useful and appropriate.

02:39 For part d, the r squared that it gives me, i would literally just take my r value and square it, but it is .83 .92.

02:53 Sometimes they like that in a decimal, and sometimes they like it in a percentage, so we would call that like 84%, right, or 0 .84.

03:03 And whenever you're looking to interpret that, you're always looking for the percent of variation that can be explained.

03:12 Okay? so that's always the wordage that you're looking for is percent of variation there.

03:16 So we want the one that says something about percent of variation.

03:23 Okay? so not a, right? because it doesn't say anything about percent of variation.

03:31 C doesn't say anything about percent of variation.

03:35 The only thing that says anything about variation is b...

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