Question

A small school has only two 4^th grade classes and two 5^th grade classes. Each year, students at the school take the Nebraska Test of Basic Skills (NTBS) in math and Language Arts. The Excel file, 745 Project Data, contains all of the scores for a certain class tracked over their 4^th and 5^th grade years.

1. Create a frequency distribution and cumulative frequency distribution of the 4^th Grade Math test scores for all of the students. Use 5 classes.
2. Create a histogram, frequency polygon, and ogive for the 4^th Grade Math test scores for all of the students.
3. Create a box-and-whiskers plot for the 5^th Grade LA test scores for all of the students.
4. Determine whether or not students in the two 4^th grade classes have the same average scores in math, and whether or not students in the two 4^th grade classes have the same average score in language arts. For both tests, use α = 0.05.
5. It has been observed that Crenshaw’s students don’t seem to do in well in math. To investigate that, for the 19 students who had Crenshaw in 5^th grade, determine whether or not their math scores decreased from 4^th to 5^th grades. Use α = 0.0 Do the same for the 17 students who had Davis in 5^th grade. What can you conclude from these tests?
6. On the other hand, Crenshaw’s students seem to excel in language arts. To investigate that, for the 19 students who had Crenshaw in 5^th grade, determine whether or not their language arts scores increased from 4^th to 5^th grades. Use α = 0.05. Do the same for the 17 students who had Davis in 5^th grade. What can you conclude from these tests?
7. On the basis of questions 4 through 6, what would you, as an administrator, recommend regarding Crenshaw and Davis?
8. Determine whether or not there is a relationship between the math scores and the LA scores in 4th grade, and if there is a relationship between the math scores and the LA scores in 5th grade. Use α = 0.05.

Answer 1

A small school has only two 4th grade classes and two 5th grade classes. Each year, students at the school take the Nebraska Test of Basic Skills (NTBS) in math and Language Arts. The Excel file, 745 Project Data, contains all of the scores for a certain class tracked over their 4th and 5th grade years.

Create a frequency distribution and cumulative frequency distribution of the 4th Grade Math test scores for all of the students. Use 5 classes.

Smallest score is 480 and largest score is 780.

Now we have to make classes and find corresponding frequency.

SO we make class of width 70.

So first class is 450-520, next one is 520-590 and so on.

Now we have to find frequency of each class.

Frequency is the number of observations fall in the corresponding class.

So the complete frequency distribution is,

class	frequency
450-520	5
520-590	15
590-660	10
660-730	5
730-800	1
total	36

Cumulative distribution is,

class	frequency	cumulative
450-520	5	5
520-590	15	20
590-660	10	30
660-730	5	35
730-800	1	36
total	36

Create a histogram, frequency polygon, and ogive for the 4th Grade Math test scores for all of the students.

We can draw histogram in excel.

steps :

ENTER data into excel sheet --> select class and frequency --> Insert --> Columns --> 2-D column --> select first option --> right click on bars --> format data series --> adjust gap width to 0 --> close

Frequency polygon :

Excel steps :

ENTER data into excel sheet --> Insert --> Line --> 2-D line --> ok

Ogive curve :

ENTER data into excel sheet --> Insert --> Scatter --> select second option --> ok

These are the three graphs.

Create a box-and-whiskers plot for the 5th Grade LA test scores for all of the students.

We can construct boxplot in MINITAB.

steps :

ENTER data into MINITAB sheet --> Graph --> Boxplot --> Simple --> ok --> Graph variable : select data column --> ok

Determine whether or not students in the two 4th grade classes have the same average scores in math, and whether or not students in the two 4th grade

Here we have to test the hypothesis that,

H0 : mu = 650 Vs H1 : mu not= 650

mu is population mean.

By assumption we take mu = 650

Here we have given sample data so we use one sample t-test.

We can do one sample t test in MINITAB.

steps :

ENTER data into MINITAB sheet --> Stat --> Basic statistics--> one sample t --> select data column --> Perform hypothesis test --> Hypothesized mean : 650 --> options --> Confidence level : 95.0 --> Alternative hypothesis : not= --> ok -> ok

One-Sample T: math

Test of ? = 650 vs ? 650

Variable N Mean StDev SE Mean 95% CI T P
math 36 584.4 66.6 11.1 (561.9, 607.0) -5.91 0.000

Test statistic = -5.91

P-value = 0.000

P-value < alpha

Reject H0 at 5% level of significance.

COnclusion :  students in the two 4th grade classes have not same average scores in math.

SImilarly we have to do for language arts.

One-Sample T: la

Test of ? = 650 vs ? 650

Variable N Mean StDev SE Mean 95% CI T P
la 36 608.9 63.6 10.6 (587.4, 630.4) -3.88 0.000

Here also p-value < alpha (0.05)

Reject H0 at 5% level of significance.

Conclusion :  students in the two 4th grade classes have not same average scores in language arts.