A graduate teaching assistant for an Introduction to Statistics course collected data from one of her classes to investigate the relationship between using the explanatory variable x=study time per week (average number of hours) to predict the response variable y=college GPA. For the 21 females in her class, the correlation was 0.42. For the eight males in her class, the data were as shown in the following table. Complete parts a through c below. Student 1 2 3 4 5 6 7 8 Study Time 15 6 22 13 24 4 10 15 GPA 3.4 2.8 3.9 3.2 3.7 2.7 3.2 2.7 a. Construct a scatterplot. Interpret. Which scatterplot below correctly shows the data? A. 04004xy A scatterplot has a horizontal x-axis labeled from 0 to 40 in increments of 10 and a vertical y-axis labeled from 0 to 4 in increments of 1. A cluster of plotted points that form a line that rises from left to right lie between horizontal coordinates of 0 and 30 and the vertical coordinates of 2 and 4. The cluster includes (2.7, 4), (2.7, 15), and (2.8, 6). Your answer is correct. B. 04004xy A scatterplot has a horizontal x-axis labeled from 0 to 40 in increments of 10 and a vertical y-axis labeled from 0 to 4 in increments of 1. A cluster of plotted points that form a line that falls from left to right lie between horizontal coordinates of 0 and 30 and the vertical coordinates of 2 and 4. The cluster includes (10, 2.7), (24, 3.2), and (15, 3.9). C. 04004xy A scatterplot has a horizontal x-axis labeled from 0 to 40 in increments of 10 and a vertical y-axis labeled from 0 to 4 in increments of 1. A cluster of plotted points that form a line that falls from left to right lie between horizontal coordinates of 0 and 30 and the vertical coordinates of 2 and 4. The cluster includes (4, 3.7), (10, 2.8), and (15, 3.9). D. 04004xy A scatterplot has a horizontal x-axis labeled from 0 to 40 in increments of 10 and a vertical y-axis labeled from 0 to 4 in increments of 1. A cluster of plotted points that form a line that falls from left to right lie between horizontal coordinates of 0 and 30 and the vertical coordinates of 2 and 4. The cluster includes (10, 3.2), (24, 2.8), and (22, 3.9). The scatterplot shows a strong positive association between the two variables. b. Find and interpret the correlation. The correlation is 0.830.83. (Round to two decimal places as needed.) The correlation shows a strong positive association between the two variables, with longer study times associated with higher GPAs. c. Find and interpret the prediction equation by reporting the predicted GPA for a student who studies (i) 9 hours per week, (ii) 24 hours per week. The regression equation is y=nothing+x. (Round to two decimal places as needed.) Enter your answer in the edit fields and then click Check Answer.

A graduate teaching assistant for an Introduction to Statistics course collected data from one of her classes to investigate the relationship between using the explanatory variable x=study time per week (average number of hours) to predict the response variable y=college GPA. For the 21 females in her class, the correlation was 0.42. For the eight males in her class, the data were as shown in the following table. Complete parts a through c below. Student 1 2 3 4 5 6 7 8 Study Time 15 6 22 13 24 4 10 15 GPA 3.4 2.8 3.9 3.2 3.7 2.7 3.2 2.7 a. Construct a scatterplot. Interpret. Which scatterplot below correctly shows the data? A. 04004xy A scatterplot has a horizontal x-axis labeled from 0 to 40 in increments of 10 and a vertical y-axis labeled from 0 to 4 in increments of 1. A cluster of plotted points that form a line that rises from left to right lie between horizontal coordinates of 0 and 30 and the vertical coordinates of 2 and 4. The cluster includes (2.7, 4), (2.7, 15), and (2.8, 6). Your answer is correct. B. 04004xy A scatterplot has a horizontal x-axis labeled from 0 to 40 in increments of 10 and a vertical y-axis labeled from 0 to 4 in increments of 1. A cluster of plotted points that form a line that falls from left to right lie between horizontal coordinates of 0 and 30 and the vertical coordinates of 2 and 4. The cluster includes (10, 2.7), (24, 3.2), and (15, 3.9). C. 04004xy A scatterplot has a horizontal x-axis labeled from 0 to 40 in increments of 10 and a vertical y-axis labeled from 0 to 4 in increments of 1. A cluster of plotted points that form a line that falls from left to right lie between horizontal coordinates of 0 and 30 and the vertical coordinates of 2 and 4. The cluster includes (4, 3.7), (10, 2.8), and (15, 3.9). D. 04004xy A scatterplot has a horizontal x-axis labeled from 0 to 40 in increments of 10 and a vertical y-axis labeled from 0 to 4 in increments of 1. A cluster of plotted points that form a line that falls from left to right lie between horizontal coordinates of 0 and 30 and the vertical coordinates of 2 and 4. The cluster includes (10, 3.2), (24, 2.8), and (22, 3.9). The scatterplot shows a strong positive association between the two variables. b. Find and interpret the correlation. The correlation is 0.830.83. (Round to two decimal places as needed.) The correlation shows a strong positive association between the two variables, with longer study times associated with higher GPAs. c. Find and interpret the prediction equation by reporting the predicted GPA for a student who studies (i) 9 hours per week, (ii) 24 hours per week. The regression equation is y=nothing+x. (Round to two decimal places as needed.) Enter your answer in the edit fields and then click Check Answer.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 15PPS

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Question

A graduate teaching assistant for an Introduction to Statistics course collected data from one of her classes to investigate the relationship between using the explanatory variable

x=study

time per week (average number of hours) to predict the response variable

y=college

GPA. For the 21 females in her class, the correlation was 0.42. For the eight males in her class, the data were as shown in the following table. Complete parts a through c below.

Student	1	2	3	4	5	6	7	8
Study Time	15	6	22	13	24	4	10	15
GPA	3.4	2.8	3.9	3.2	3.7	2.7	3.2	2.7

a. Construct a scatterplot. Interpret.

Which scatterplot below correctly shows the data?

04004xy

A scatterplot has a horizontal x-axis labeled from 0 to 40 in increments of 10 and a vertical y-axis labeled from 0 to 4 in increments of 1. A cluster of plotted points that form a line that rises from left to right lie between horizontal coordinates of 0 and 30 and the vertical coordinates of 2 and 4. The cluster includes (2.7, 4), (2.7, 15), and (2.8, 6).

Your answer is correct.

04004xy

A scatterplot has a horizontal x-axis labeled from 0 to 40 in increments of 10 and a vertical y-axis labeled from 0 to 4 in increments of 1. A cluster of plotted points that form a line that falls from left to right lie between horizontal coordinates of 0 and 30 and the vertical coordinates of 2 and 4. The cluster includes (10, 2.7), (24, 3.2), and (15, 3.9).

04004xy

A scatterplot has a horizontal x-axis labeled from 0 to 40 in increments of 10 and a vertical y-axis labeled from 0 to 4 in increments of 1. A cluster of plotted points that form a line that falls from left to right lie between horizontal coordinates of 0 and 30 and the vertical coordinates of 2 and 4. The cluster includes (4, 3.7), (10, 2.8), and (15, 3.9).

04004xy

A scatterplot has a horizontal x-axis labeled from 0 to 40 in increments of 10 and a vertical y-axis labeled from 0 to 4 in increments of 1. A cluster of plotted points that form a line that falls from left to right lie between horizontal coordinates of 0 and 30 and the vertical coordinates of 2 and 4. The cluster includes (10, 3.2), (24, 2.8), and (22, 3.9).

The scatterplot shows

a strong positive

association between the two variables.

b. Find and interpret the correlation.

The correlation is

0.830.83.

(Round to two decimal places as needed.)

The correlation shows

a strong positive

association between the two variables, with longer study times associated with

higher

GPAs.

c. Find and interpret the prediction equation by reporting the predicted GPA for a student who studies (i)

hours per week, (ii)

hours per week.

The regression equation is

y=nothing+x.

(Round to two decimal places as needed.)

Enter your answer in the edit fields and then click Check Answer.

Expert Solution

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In this case, the independent variable is study time per week (x) and the dependent variable is college GPA (y).

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