Test scores of students in one large Statistics class are normally distributed w
ID: 3248539 • Letter: T
Question
Test scores of students in one large Statistics class are normally distributed with a mean of 80 and a 1. If one student from the class is randomly selected, what is the probability that his/her test score is below 76 using empirical rule? 2. If one student from the class is randomly selected, what is the probability that his/her test score is above 86 using the z-table? If one student from the class is randomly selected, what is the probability that his/her test score is either below 70 or above 86 using the z-table? 4. If 40 students are randomly selected from the class, what is the probability that their average test scores is below 78? A professor is interested in knowing if the score on the first test can be used to predict score on the final exam in an elementary statistics course. He randomly selected 8 students and got the following data: 1. Compute and interpret the correlation coefficient between the two variables. 2. Using the equation of the regression line, what will be the predicted final exam score of a student whose first test score is 120? In a study to determine if gender and level of physical activity are related, researchers obtained the following data 1. What percent of the individuals in the study are females who engage in high physical activity? 2. Calculate and interpret the value of the chi-squared test statistic. What is the conclusion of the test?Explanation / Answer
Problem-E I am not doing because standard deviation value is not in the image
Problem-F
From following results correlation=-0.1651
Regression line Y=177.0037-0.1414*X
So predicted score=177.0037-0.1414*120 =160.0357
S.No.
First Test Score (X)
Final Exam1Score (Y)
x^2
y^2
xy
1
153
145
23409
21025
22185
2
144
140
20736
19600
20160
3
162
145
26244
21025
23490
4
149
170
22201
28900
25330
5
127
145
16129
21025
18415
6
118
175
13924
30625
20650
7
158
170
24964
28900
26860
8
163
160
26569
25600
26080
Total
1174
1250
174176
196700
183170
Mean
146.75
156.25
SD
16.44
14.08
Correlation=(Sum(xy)-nMeanx*Meany)/(sqrt(Sumx^2-n*Meanx^2)*(Sumy^2-n*Meany^2))
-0.1651
Slope=r*sy/sx
-0.1414
Intercept=Meany-slope*meanx
177.0037
Problem-G
Part-1-P(Female and High)=38/(20+92+41+38)=0.1990
Part-2-From following results chi-square test statistic =24.69591 with p-value=6.71E-07
As p-value is less than 0.001 we conclude that physical activity depends on gender
Chi-Square Test
Observed Frequencies
Physical
Calculations
Gender
Low
High
Total
fo-fe
Male
20
92
112
-15.7696
15.76963
Female
41
38
79
15.76963
-15.7696
Total
61
130
191
Expected Frequencies
Physical
Gender
Low
High
Total
(fo-fe)^2/fe
Male
35.76963
76.23037
112
6.952303
3.262235
Female
25.23037
53.76963
79
9.85643
4.62494
Total
61
130
191
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
2
Degrees of Freedom
1
Results
Critical Value
3.841459
Chi-Square Test Statistic
24.69591
p-Value
6.71E-07
Reject the null hypothesis
S.No.
First Test Score (X)
Final Exam1Score (Y)
x^2
y^2
xy
1
153
145
23409
21025
22185
2
144
140
20736
19600
20160
3
162
145
26244
21025
23490
4
149
170
22201
28900
25330
5
127
145
16129
21025
18415
6
118
175
13924
30625
20650
7
158
170
24964
28900
26860
8
163
160
26569
25600
26080
Total
1174
1250
174176
196700
183170
Mean
146.75
156.25
SD
16.44
14.08
Correlation=(Sum(xy)-nMeanx*Meany)/(sqrt(Sumx^2-n*Meanx^2)*(Sumy^2-n*Meany^2))
-0.1651
Slope=r*sy/sx
-0.1414
Intercept=Meany-slope*meanx
177.0037
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