Data handling <\/p>\n
a. Below is the data view of the dataset<\/p>\n
b. Shown below is the variable view of the dataset<\/p>\n
2. Descriptive statistics<\/p>\n
The process and results of obtaining descriptive statistics of continuous variables are as below. The mean \u00b1 standard deviation of age, exam marks, assignment marks, and IQ are 20.50 \u00b1 1.842, 82.79 \u00b1 12.594, 81.88 \u00b1 10.695, 105.17 \u00b1 16.282 respectively<\/p>\n
Descriptive Statistics<\/p>\n
N<\/p>\n
Minimum<\/p>\n
Maximum<\/p>\n
Mean<\/p>\n
Std. Deviation<\/p>\n
Age<\/p>\n
24<\/p>\n
18<\/p>\n
24<\/p>\n
20.50<\/p>\n
1.842<\/p>\n
Exam Marks (for a maximum of 100)<\/p>\n
24<\/p>\n
55<\/p>\n
99<\/p>\n
82.79<\/p>\n
12.594<\/p>\n
Assignment Marks (for a maximum of 100)<\/p>\n
24<\/p>\n
55<\/p>\n
95<\/p>\n
81.88<\/p>\n
10.695<\/p>\n
intelligence quotient<\/p>\n
24<\/p>\n
72<\/p>\n
136<\/p>\n
105.17<\/p>\n
16.282<\/p>\n
Valid N (listwise)<\/p>\n
24<\/p>\n
The chart below shows gender is coded as 0 or 1<\/p>\n
The following are the process and results of descriptive statistics for categorical variables. There were more females (58.3) than males. (41.7). Observe from the table that juniors (33) had the most frequency followed closely by a sophomore (29) while seniors (8) had the least frequency.<\/p>\n
Sex (M=Male, F=Female)<\/p>\n
Frequency<\/p>\n
Per cent<\/p>\n
Valid Percent<\/p>\n
Cumulative Percent<\/p>\n
Valid<\/p>\n
Male<\/p>\n
10<\/p>\n
41.7<\/p>\n
41.7<\/p>\n
41.7<\/p>\n
Female<\/p>\n
14<\/p>\n
58.3<\/p>\n
58.3<\/p>\n
100.0<\/p>\n
Total<\/p>\n
24<\/p>\n
100.0<\/p>\n
100.0<\/p>\n
Year in College (1=Freshman; 2=Sophomore; 3=Junior; 4=Senior)<\/p>\n
Frequency<\/p>\n
Percent<\/p>\n
Valid Percent<\/p>\n
Cumulative Percent<\/p>\n
Valid<\/p>\n
Freshman<\/p>\n
5<\/p>\n
20.8<\/p>\n
20.8<\/p>\n
20.8<\/p>\n
Sophomore<\/p>\n
7<\/p>\n
29.2<\/p>\n
29.2<\/p>\n
50.0<\/p>\n
Junior<\/p>\n
8<\/p>\n
33.3<\/p>\n
33.3<\/p>\n
83.3<\/p>\n
Senior<\/p>\n
2<\/p>\n
8.3<\/p>\n
8.3<\/p>\n
91.7<\/p>\n
20<\/p>\n
1<\/p>\n
4.2<\/p>\n
4.2<\/p>\n
95.8<\/p>\n
30<\/p>\n
1<\/p>\n
4.2<\/p>\n
4.2<\/p>\n
100.0<\/p>\n
Total<\/p>\n
24<\/p>\n
100.0<\/p>\n
100.0<\/p>\n
The pie chart below shows the distribution for years in College. <\/p>\n
The histogram for IQ is created as below. The data follows the normal distribution. <\/p>\n
The scatter plot of exam marks versus IQ below shows a linear association between the two. <\/p>\n
The scatter plot of IQ versus sex is shown below. The IQ of females is distributed higher those that of males. <\/p>\n
h. The difference in the mean IQ per gender is as below. Males have a lower mean IQ (94.5) than their female (112.79) counterparts. <\/p>\n
Mean IQ for each gender<\/p>\n
Mean <\/p>\n
Sex (M=Male, F=Female)<\/p>\n
intelligence quotient<\/p>\n
Male<\/p>\n
94.50<\/p>\n
Female<\/p>\n
112.79<\/p>\n
Total<\/p>\n
105.17<\/p>\n
Data analysis<\/p>\n
The analysis and result of the One-Sample T-test are shown below.<\/p>\n
Null hypothesis: exam marks are not significantly larger than 75<\/p>\n
The p-value (.006) is less than a 5% significance level therefore the null is rejected. Hence exam marks are significantly larger than 75<\/p>\n
One-Sample Statistics<\/p>\n
N<\/p>\n
Mean<\/p>\n
Std. Deviation<\/p>\n
Std. Error Mean<\/p>\n
Exam Marks<\/p>\n
24<\/p>\n
82.79<\/p>\n
12.594<\/p>\n
2.571<\/p>\n
One-Sample Test<\/p>\n
Test Value = 75<\/p>\n
t<\/p>\n
df<\/p>\n
Sig. (2-tailed)<\/p>\n
Mean Difference<\/p>\n
95% Confidence Interval of the Difference<\/p>\n
Lower<\/p>\n
Upper<\/p>\n
Exam Marks<\/p>\n
3.031<\/p>\n
23<\/p>\n
.006<\/p>\n
7.792<\/p>\n
2.47<\/p>\n
13.11<\/p>\n
The following is the analysis and result of the Independent samples t-test <\/p>\n
Null hypothesis: There are no significant differences in the exam marks between men and women. The p-value (.001) is less than a 5% significance level therefore the null is rejected. Hence there are significant differences in the exam marks between men and women.<\/p>\n
Group Statistics<\/p>\n
Sex (M=Male, F=Female)<\/p>\n
N<\/p>\n
Mean<\/p>\n
Std. Deviation<\/p>\n
Std. Error Mean<\/p>\n
Exam Marks (for a maximum of 100)<\/p>\n
Male<\/p>\n
10<\/p>\n
72.90<\/p>\n
13.153<\/p>\n
4.159<\/p>\n
Female<\/p>\n
14<\/p>\n
89.86<\/p>\n
5.641<\/p>\n
1.508<\/p>\n
Independent Samples Test<\/p>\n
Levene’s Test for Equality of Variances<\/p>\n
t-test for Equality of Means<\/p>\n
F<\/p>\n
Sig.<\/p>\n
t<\/p>\n
df<\/p>\n
Sig. (2-tailed)<\/p>\n
Mean Difference<\/p>\n
Std. Error Difference<\/p>\n
95% Confidence Interval of the Difference<\/p>\n
Lower<\/p>\n
Upper<\/p>\n
Exam Marks <\/p>\n
Equal variances assumed<\/p>\n
14.459<\/p>\n
.001<\/p>\n
-4.327<\/p>\n
22<\/p>\n
.000<\/p>\n
-16.957<\/p>\n
3.919<\/p>\n
-25.084<\/p>\n
-8.830<\/p>\n
Equal variances not assumed<\/p>\n
-3.833<\/p>\n
11.385<\/p>\n
.003<\/p>\n
-16.957<\/p>\n
4.424<\/p>\n
-26.654<\/p>\n
-7.260<\/p>\n
Shown below is the process and result obtained from running a paired samples t-test. <\/p>\n
Null hypothesis: There is no significant difference between the exam marks and the assignment marks. The p-value (.659) is greater than the 5% significance level therefore the null is not rejected. Hence there is no significant difference between the exam marks and the assignment marks.<\/p>\n
Paired Samples Statistics<\/p>\n
Mean<\/p>\n
N<\/p>\n
Std. Deviation<\/p>\n
Std. Error Mean<\/p>\n
Pair 1<\/p>\n
Exam Marks<\/p>\n
82.79<\/p>\n
24<\/p>\n
12.594<\/p>\n
2.571<\/p>\n
Assignment Marks<\/p>\n
81.88<\/p>\n
24<\/p>\n
10.695<\/p>\n
2.183<\/p>\n
Paired Samples Correlations<\/p>\n
N<\/p>\n
Correlation<\/p>\n
Sig.<\/p>\n
Pair 1<\/p>\n
Exam Marks & Assignment Marks <\/p>\n
24<\/p>\n
.638<\/p>\n
.001<\/p>\n
Paired Samples Test<\/p>\n
Paired Differences<\/p>\n
t<\/p>\n
df<\/p>\n
Sig. (2-tailed)<\/p>\n
Mean<\/p>\n
Std. Deviation<\/p>\n
Std. Error Mean<\/p>\n
95% Confidence Interval of the Difference<\/p>\n
Lower<\/p>\n
Upper<\/p>\n
Pair 1<\/p>\n
Exam Marks – Assignment Marks<\/p>\n
.917<\/p>\n
10.056<\/p>\n
2.053<\/p>\n
-3.330<\/p>\n
5.163<\/p>\n
.447<\/p>\n
23<\/p>\n
.659<\/p>\n
d. The correlation analysis and result between gender, IQ, exam and assignment marks are as below. All the correlations are significant at a 5% significance level. Exam marks are positively and highly correlated to assignment marks and sex but moderately correlated to IQ. Similarly, assignment marks are positively and highly correlated to IQ but moderately correlated to sex.<\/p>\n
Correlations<\/p>\n
Exam Marks (for a maximum of 100)<\/p>\n
Assignment Marks (for a maximum of 100)<\/p>\n
intelligence quotient<\/p>\n
Sex (M=Male, F=Female)<\/p>\n
Exam Marks (for a maximum of 100)<\/p>\n
Pearson Correlation<\/p>\n
1<\/p>\n
.638**<\/p>\n
.461*<\/p>\n
.678**<\/p>\n
Sig. (2-tailed)<\/p>\n
.001<\/p>\n
.023<\/p>\n
.000<\/p>\n
N<\/p>\n
24<\/p>\n
24<\/p>\n
24<\/p>\n
24<\/p>\n
Assignment Marks (for a maximum of 100)<\/p>\n
Pearson Correlation<\/p>\n
.638**<\/p>\n
1<\/p>\n
.768**<\/p>\n
.450*<\/p>\n
Sig. (2-tailed)<\/p>\n
.001<\/p>\n
.000<\/p>\n
.027<\/p>\n
N<\/p>\n
24<\/p>\n
24<\/p>\n
24<\/p>\n
24<\/p>\n
intelligence quotient<\/p>\n
Pearson Correlation<\/p>\n
.461*<\/p>\n
.768**<\/p>\n
1<\/p>\n
.566**<\/p>\n
Sig. (2-tailed)<\/p>\n
.023<\/p>\n
.000<\/p>\n
.004<\/p>\n
N<\/p>\n
24<\/p>\n
24<\/p>\n
24<\/p>\n
24<\/p>\n
Sex (M=Male, F=Female)<\/p>\n
Pearson Correlation<\/p>\n
.678**<\/p>\n
.450*<\/p>\n
.566**<\/p>\n
1<\/p>\n
Sig. (2-tailed)<\/p>\n
.000<\/p>\n
.027<\/p>\n
.004<\/p>\n
N<\/p>\n
24<\/p>\n
24<\/p>\n
24<\/p>\n
24<\/p>\n
**. Correlation is significant at the 0.01 level (2-tailed).<\/p>\n
*. Correlation is significant at the 0.05 level (2-tailed).<\/p>\n
The dummy coding for IQ is implemented as below. IQ lower than 105 is 0 while IQ higher than 105 is 1.<\/p>\n
Do a multiple regression analysis to explain the variance in assignment marks using the independent variables of age; sex; and IQ (dummy coded) and interpret the results. <\/p>\n
The following is the ANOVA for the regression. <\/p>\n
Null hypothesis: The model is not significant.<\/p>\n
The p-value (.005) is less than a 5% significance level therefore the null is rejected. Hence the model is significant. <\/p>\n
ANOVA<\/p>\n
Model<\/p>\n
Sum of Squares<\/p>\n
df<\/p>\n
Mean Square<\/p>\n
F<\/p>\n
Sig.<\/p>\n
1<\/p>\n
Regression<\/p>\n
1212.291<\/p>\n
3<\/p>\n
404.097<\/p>\n
5.698<\/p>\n
.005b<\/p>\n
Residual<\/p>\n
1418.334<\/p>\n
20<\/p>\n
70.917<\/p>\n
Total<\/p>\n
2630.625<\/p>\n
23<\/p>\n
a. Dependent Variable: Assignment Marks (for a maximum of 100)<\/p>\n
b. Predictors: (Constant), Year in College (1=Freshman; 2=Sophomore; 3=Junior; 4=Senior), iQ(Dummy coded), Sex (M=Male, F=Female)<\/p>\n
The coefficients table for the analysis is shown below.<\/p>\n
Null hypothesis: The respective model coefficients are not significant in the model. Only the constant and IQ coefficients are significant in the model. Their p-values were 0.00 and 0.017 respectively warranting the rejection of their respective null hypotheses. <\/p>\n
Coefficients<\/p>\n
Model<\/p>\n
Unstandardized Coefficients<\/p>\n
Standardized Coefficients<\/p>\n
t<\/p>\n
Sig.<\/p>\n
B<\/p>\n
Std. Error<\/p>\n
Beta<\/p>\n
1<\/p>\n
(Constant)<\/p>\n
78.149<\/p>\n
3.321<\/p>\n
23.534<\/p>\n
.000<\/p>\n
iQ(Dummy coded)<\/p>\n
12.125<\/p>\n
4.669<\/p>\n
.579<\/p>\n
2.597<\/p>\n
.017<\/p>\n
Sex (M=Male, F=Female)<\/p>\n
-.757<\/p>\n
4.869<\/p>\n
-.036<\/p>\n
-.156<\/p>\n
.878<\/p>\n
Year in College (1=Freshman; 2=Sophomore; 3=Junior; 4=Senior)<\/p>\n
-.450<\/p>\n
.281<\/p>\n
-.279<\/p>\n
-1.600<\/p>\n
.125<\/p>\n
a. Dependent Variable: Assignment Marks (for a maximum of 100)<\/p>\n
The r-squared shows that 67.9% of the variations of assignment marks are explained in the model.<\/p>\n
Model Summary<\/p>\n
Model<\/p>\n
R<\/p>\n
R Square<\/p>\n
Adjusted R Square<\/p>\n
Std. Error of the Estimate<\/p>\n
1<\/p>\n
.679a<\/p>\n
.461<\/p>\n
.380<\/p>\n
8.421<\/p>\n
a. Predictors: (Constant), Year in College (1=Freshman; 2=Sophomore; 3=Junior; 4=Senior), iQ(Dummy coded), Sex (M=Male, F=Female)<\/p>\n","protected":false},"excerpt":{"rendered":"
Data handling a. Below is the data view of the dataset b. Shown below is the variable view of the dataset 2. Descriptive statistics The process and results of obtaining descriptive statistics of continuous variables are as below. The mean \u00b1 standard deviation of age, exam marks, assignment marks, and IQ are 20.50 \u00b1 1.842, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[10],"class_list":["post-96286","post","type-post","status-publish","format-standard","hentry","category-research-paper-writing","tag-writing"],"_links":{"self":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts\/96286","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/comments?post=96286"}],"version-history":[{"count":0,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts\/96286\/revisions"}],"wp:attachment":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/media?parent=96286"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/categories?post=96286"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/tags?post=96286"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}