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

## # A tibble: 6 × 6
##   `Course Taken`            Frequency `Mean Intrinsic5` Mean E…¹ Mean …² Mean …³
##   <chr>                         <int>             <dbl>    <dbl>   <dbl>   <dbl>
## 1 BS Biology                       33              4.94     5.27    3.88   NA   
## 2 BS Civil Engineering             16              4.06     5.5     3.31    4.38
## 3 BS Electrical Engineering        17              4.35     5       3.47    3.71
## 4 BS Mathematics                   33              4.27     5.39    3.55    3.52
## 5 BSED Biology                     32              4.34     5.22    3.25    3.62
## 6 BSED English                     32              4.19     5.66    3.91    3.03
## # … with abbreviated variable names ¹​`Mean Extrinsic4`, ²​`Mean TP3`,
## #   ³​`Mean CP3`

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'. You can override using the `.groups`
## argument.
## # A tibble: 5 × 3
## # Groups:   In3 [1]
##   In3            In4              count
##   <chr>          <chr>            <int>
## 1 Strongly Agree Agree                9
## 2 Strongly Agree Disagree             2
## 3 Strongly Agree Moderately Agree     3
## 4 Strongly Agree Neutral              7
## 5 Strongly Agree Strongly Agree      12

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'. You can override using the `.groups`
## argument.
## # A tibble: 1 × 3
## # Groups:   In3 [1]
##   In3            In4     count
##   <chr>          <chr>   <int>
## 1 Strongly Agree Neutral     7

Answer: There is 7 observation in Variable In3 that are strongly agree and at the same time Neutral in variable 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.

Make two groups of the variable “Course Taken”,

Grouping: Group 1 with courses: BS Civil Engineering, BS Electrical Engineering, and BS Mathematics Group 2: BS Biology, BSED Biology, and BSED English

## # A tibble: 163 × 35
##      Age Gender Course T…¹   In1   In2   In3   In4   In5   In6   In7   In8   Ex1
##    <dbl> <chr>  <chr>      <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
##  1    22 Female BS Mathem…     4     3     2     1     4     7     6     7     4
##  2    23 Female BS Biology     6     6     4     4     4     5     4     7     4
##  3    20 Female BSED Engl…     5     5     3     3     2     6     5     7     5
##  4    22 Female BSED Biol…     4     5     4     3     3     6     6     7     5
##  5    23 Male   BSED Engl…     7     6     5     5     4     6     4     7     7
##  6    22 Female BSED Biol…     6     6     6     6     6     7     7     7     7
##  7    20 Male   BS Civil …     4     5     6     2     5     7     4     1     7
##  8    21 Female BS Electr…     5     6     5     6     5     7     6     7     7
##  9    21 Female BS Mathem…     6     7     5     5     5     7     7     7     7
## 10    22 Male   BS Biology     6     7     5     6     7     7     7     7     5
## # … with 153 more rows, 23 more variables: Ex2 <dbl>, Ex3 <dbl>, Ex4 <dbl>,
## #   Ex5 <dbl>, Ex6 <dbl>, Ex7 <dbl>, Ex8 <dbl>, Ex9 <dbl>, Ex10 <dbl>,
## #   Ex11 <dbl>, TP1 <dbl>, TP2 <dbl>, TP3 <dbl>, TP4 <dbl>, TP5 <dbl>,
## #   T6 <dbl>, CP1 <dbl>, CP2 <dbl>, CP3 <dbl>, CP4 <dbl>, CP5 <dbl>,
## #   CTrecode <chr>, GroupofCourse <chr>, and abbreviated variable name
## #   ¹​`Course Taken`

3.1 Is there a significant difference between the two groups of course taken in terms of the variable “InAverage”? (Note: 1.1 Check first the equality of variances 1.2 Answer this by including all the steps in hypothesis testing)

## 
## Group1 Group2 
##     66     97

Checking the equality of variances

## 
##  F test to compare two variances
## 
## data:  InAverage by Data_Course$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: In terms of the variable “InAverage,” there is no significance difference between the two groups of courses that were taken.

Alternative Hypothesis: In terms of the variable “InAverage,” there is a considerable variation between the two groups of courses taken.

The p-value is 0.2458, which is greater than the level of significance (0.05), indicating that there is no difference between the two groups of courses taken in terms of the variable “InAverage” in the results. The null hypothesis is therefore accepted.

4. Is there a significant difference among the courses taken in terms of the variable “InAverage”(Refer to Q3 for the “Inaverage” variable)? (Note: 1. Answer this by using F-test 1.2 Answer this by including all the steps in hypothesis testing 1.3 Provide results for pairwise comparison if significant)

##                 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 discernible difference between the taken courses in terms of InAverage.

Alternative Hypothesis: In terms of InAverage, there is a huge difference in the courses taken.

Interpretation: The p-value is 0.904, which exceeds the 0.05 significance level, and the result demonstrates that there is no significant difference between the courses completed in terms of the variable “InAverage.” The null hypothesis is therefore accepted.