1.1 First output:

## # A tibble: 6 × 4
##   `Course Taken`            Frequency `Mean Age` `SD of Age`
##   <chr>                         <int>      <dbl>       <dbl>
## 1 BS Biology                       33       21.6       0.751
## 2 BS Civil Engineering             16       21.4       0.727
## 3 BS Electrical Engineering        17       21.6       0.618
## 4 BS Mathematics                   33       21.7       0.924
## 5 BSED Biology                     32       21.5       0.803
## 6 BSED English                     32       21.6       0.878

1.2 Second output:

Consider the variables: In4, Ex3, TP3, and CP3 that are grouped according to “course taken”

## # A tibble: 6 × 6
##   `Course Taken`        Frequency `Mean Intrinsic5` `Mean Extrinsic4` `Mean TP3`
##   <chr>                     <int>             <dbl>             <dbl>      <dbl>
## 1 BS Biology                   33              4.94              5.27       3.88
## 2 BS Civil Engineering         16              4.06              5.5        3.31
## 3 BS Electrical Engine…        17              4.35              5          3.47
## 4 BS Mathematics               33              4.27              5.39       3.55
## 5 BSED Biology                 32              4.34              5.22       3.25
## 6 BSED English                 32              4.19              5.66       3.91
## # ℹ 1 more variable: `Mean CP3` <dbl>

Recoding the responses in Variables “In3 and In4” with the following changes:

“1 for”Strong Disagree”
“2” for “Disagree”
“3” for “Moderately Disagree”
“4” for “Neutral”
“5” for “Moderately Agree”
“6” for “Agree” “7” for “Strongly Agree”

2.1 Answer the following:

a. How many observations in Variable In3 that are strongly agree and at the same time moderately disagree in variable In4?

## `summarise()` has grouped output by 'In3.1'. You can override using the
## `.groups` argument.
## # A tibble: 4 × 3
## # Groups:   In3.1 [1]
##   In3.1          In4.1            count
##   <chr>          <chr>            <int>
## 1 Strongly Agree Agree                4
## 2 Strongly Agree Moderately Agree     3
## 3 Strongly Agree Neutral              1
## 4 Strongly Agree Strongly Agree       5

Answer: There are no observations from variable In3 that are strongly agree at the same time moderately disagree in In4.

b. How many observations in Variable In3 that are strongly agree and at the same time Neutral in variable In4?

## `summarise()` has grouped output by 'In3.1'. You can override using the
## `.groups` argument.
## # A tibble: 1 × 3
## # Groups:   In3.1 [1]
##   In3.1          In4.1   count
##   <chr>          <chr>   <int>
## 1 Strongly Agree Neutral     1

Answer: There are 1 observations in variable In3 that are strongly agree at the same time Neutral in In4.

3. Consider the following:

Make a new variable named as “InAverage”, InAverage is the average of the responses in the variables In1, In2, In3, In4, and In5.

InAverage<-(Finally$In1+Finally$In2+Finally$In3+Finally$In4+Finally$In5)/5

Make two groups of the variable “Course Taken”
Grouping:
Group 1: BS Civil Engineering, BS Electrical Engineering, ad BS Mathematics
Group 2: BS Biology, BSED Biology, and BSED English

3.1 Is there a significant difference between the two groups of courses taken in terms of the variable “InAverage”?

## 
## Group1 Group2 
##     66     97

Checking the equality of Variances

## 
##  F test to compare two variances
## 
## data:  InAverage by FCourse$GroupofCourse
## F = 0.763, num df = 65, denom df = 96, p-value = 0.2458
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.4919799 1.2067147
## sample estimates:
## ratio of variances 
##           0.762995

Null hypothesis: There is no significant difference between the two groups of courses taken in terms of the variable “InAverage”

Alternative hypothesis: There is a significant difference between the two groups of courses taken in terms of the variable “InAverage”

Interpretation: The result shows that there is no significant difference between the two groups of courses taken in terms of the variable “InAverage” since the p-value is 0.2458 which exceeds the level of significance (0.05). Therefore, null hypothesis is accepted.

4.Is there a significant difference among the courses taken in terms of the variable “InAverage”(Refer to Q3 for the “Inaverage” variable)?

##                 Df Sum Sq Mean Sq F value Pr(>F)
## `Course Taken`   5   1.96  0.3913   0.314  0.904
## Residuals      157 195.87  1.2476
## Call:
##    aov(formula = InAverage ~ `Course Taken`, data = Course)
## 
## Terms:
##                 `Course Taken` Residuals
## Sum of Squares         1.95653 195.86776
## Deg. of Freedom              5       157
## 
## Residual standard error: 1.116945
## Estimated effects may be unbalanced

Null hypothesis: There is no significant difference among the courses taken in terms of InAverage

Alternative hypothesis: There is a significant difference among the courses taken in terms of InAverage

Interpretation: The result shows that there is no significant difference among the courses taken in terms of the variable “InAverage” since the p-value is 0.904 which exceeds the 0.05 significance level. Therefore, null hypothesis is accepted.