Midterm Examination

Advanced Educational Statistics

 

1.       A researcher studying Manila ethnic groups wants to determine if there is difference in income for immigrants from four different ethnic races during their first year in the city.  The data from a random sample of immigrants are presented in the table below.  Use 5 percent level of significance.

Table 1

Income of immigrants (in thousands of pesos)

                                Bicolanos                             Ilokanos                               Muslims                               Visayans

                                93.7                                        98.3                                        110.3                                     107.2

                                99.2                                        107.2                                     106.3                                     98.8

                                100.9                                     99.1                                        112.7                                     104.7

                                98.9                                        100.3                                     115.2                                     111.3

                                106.4                                                                                     109.9                                     109.8

 

2.       A new teaching method is being considered if it is found to be effective in improving the reading ability of grade one pupils.  Two groups of randomly selected pupils were given a reading test.  After the test, one of the groups (designated as experimental group) underwent eight weeks of special training while the other (designated as control group) did not.  Assume that only one teacher handled the two groups to eliminate extraneous variables concerning  teacher factor.  At the end of the 8-week period, both groups are given the reading test again.  The data are presented below.

Table 5

                Pupil                                      Experimental Group                                       Control Group

                                                Pretest                 Posttest                               Pretest                 Posttest

                1                              26                           38                                           47                           48

                2                              36                           42                                           35                           37

                3                              49                           50                                           37                           47

                4                              27                           36                                           34                           38

                5                              32                           34                                           28                           31

                6                              26                           30                                           29                           30

                7                              36                           41                                           31                           38

                8                              29                           49                                           33                           48

                9                              26                           41                                           44                           46

                10                           47                           49                                           31                           37

                11                           17                           20                                           15                           30

                12                           19                           34                                           16                           31

                13                           21                           34                                           17                           20

                14                           20                           32                                           28                           30

                15                           17                           34                                           34                           37

Using 0.01 level of significance and a non-directional test, test the difference of the following: a) Pretest scores between the experimental group and control group; b) Posttest scores between  the experimental group and control group; c) Pretest and posttest scores (mean gain scores) of the experiemental group; d) Pretest and posttest scores (mean gain scores) of the control group; e) The mean gain scores between the experimental group and the control group.

3.        Determine if significant significant difference exists between the perceptions of teachers and students on the following situations that may cause pupils’ low level of competency in Mathematics.  Use alpha = 0.05

Table 6

                                                Pupil factors that may cause Pupils’ Low Level of Competency in Mathematics

                Causes                                                                  Teachers                                              Pupils

1.       Poor health                                                                        21           50.74                     378                         76.43

2.       Poor study habit                                                               23           58.15                     487                         96.10

3.       Inadequate parents’ support in his studies          35           82.59                     434                         86.53

4.       Poor comprehension                                                     27           69.26                     431                         85.99

5.       Inadequate basic mathematical skills                      32           91.48                     478                         94.48

 

4.       A language proficiency test was given to 65 Liberal Arts and 59 Business Administration freshmen.  The Liberal Arts students got a  mean score of 88 with a standard deviation of 21.  The Business Administration students got a mean score of 82 with a standard deviation of 22.  Is there a reason to believe that there is significant difference in the performance of the two groups of students.  Use alpha = 0.05.

5.       Problem: What was the overall performance of the student teachers in on-campus training?

Table 10

                                     Over-all Performance of Students Teacher in On-Campus Teaching

                Performance Rating                        Description                                         Number                               percent

                97 – 100                                                Very Superior                                    0

                94 – 96                                                  Superior                                               30

                91 – 93                                                  Very Good                                          50

                88 – 90                                                  Good                                                     19

                85 – 87                                                  Fairly Good                                         12

                80 – 84                                                  Fair                                                         1

                75 – 79                                                  Passing                                                 1

                70 – 74                                                  Needs Improvement                     0

                Total

Solve for the mean, standard deviation, and percentage of the data.  Interpret the results.