STATISTICS EDR 8101-Lilly collects data on a sample of 40 high school students to evaluate

Question
scroll down and explain where the 15.5 and the 4.5 numbers in the parenthesis are coming from. I’m lost!

Problem 3)

Lilly collects data on a sample of 40 high school students to evaluate whether the proportion of female high school students who take advanced math courses in high school varies depending upon whether they have been raised primarily by their father or by both their mother and their father. Two variables are found below in the data file: math (0 = no advanced math and 1 = some advanced math) and Parent (1= primarily father and 2 = father and mother).

Parent Math

1.0 0.0

1.0 0.0

1.0 0.0

1.0 0.0

1.0 0.0

1.0 0.0

1.0 0.0

1.0 0.0

1.0 0.0

1.0 0.0

1.0 0.0

1.0 0.0

1.0 0.0

1.0 0.0

1.0 0.0

1.0 0.0

1.0 0.0

1.0 0.0

1.0 0.0

1.0 0.0

2.0 0.0

2.0 1.0

2.0 1.0

2.0 1.0

2.0 1.0

2.0 1.0

2.0 1.0

2.0 1.0

2.0 1.0

2.0 1.0

2.0 0.0

2.0 0.0

2.0 0.0

2.0 0.0

2.0 0.0

2.0 0.0

2.0 0.0

2.0 0.0

2.0 0.0

2.0 0.0

Conduct a crosstabs analysis to examine the proportion of female high school students who take advanced math courses is different for different levels of the parent variable.

Based on the given information of ‘Two variables are found in the data file: math (0 = no advanced math and 1 = some advanced math) and Parent (1= primarily father and 2 = father and mother)’, the following was constructed to visually represent the data in a contingency table:

No Advanced Math

Some Advanced Math

Total

Primarily Father

20

0

20

Father and Mother

11

9

20

Total

31

9

40

What percent female students took advanced math class?

To find the percentage of female students who took an advanced math class, 9 would be divided by 40 for a result of .225, or 22.5%.

What percent of female students did not take advanced math class when females were raised by just their father?

To find the percentage of female students who did not take an advanced math class when just raised by their father was 20 out of 40 which results in .5 or 50%.

What are the Chi-square results? What are the expected and the observed results that were found? Are the results of the Chi-Square significant? What do the results mean?

To find the Chi-Square statistic, first the Observed Frequency, or O, should be found. For this example, the table above may be used for these values.

The second step is to compute the Expected Frequency, or E. For this step, the following is found:

P (No Advanced Math) = 31/40 = 0.775

P (Advanced Math) = 9/40 = 0.225

P (Primarily Father) = 20/40 = 0.5

P (Father and Mother) = 20/40 = 0.5

The next step is to find the probability for each of the possible combinations using the formula P (A and B) = P(A) * P(B):

P (No Advanced Math and Primarily Father) = 0.775 * 0.5 = 0.3875

P (No Advanced Math and Father and Mother) = 0.775 * 0.5 = 0.3875

P (Advanced Math and Primarily Father) = 0.225 * 0.5 = 0.1125

P (Advanced Math and Father and Mother) = 0.225 * 0.5 = 0.1125

Next, the expected frequency is calculated by multiplying these results times the original number of students, 40. The results are placed in the following table:

No Advanced Math

Some Advanced Math

Total

Primarily Father

20 (15.5)

0 (4.5)

20 (20)

Father and Mother

11 (15.5)

9 (4.5)

20 (20)

Total

31 (31)

9 (9)

40 (40)

The Calculation of Chi-Square would be:

Outcome

O

E

O – E

(O – E)2

(O – E)2/ E

NAM/PF

20

15.5

4.5

20.25

1.30645

NAM/FandM

11

15.5

-4.5

20.25

1.30645

AM/PF

0

4.5

4.5

20.25

4.5

AM/FandM

9

4.5

-4.5

20.25

4.5

Totals

40

40.0

0.0

81.00

X2= 11.6129

For the Critical Values of Chi-Square at the 0.05 level, a 2 x 2 table size is 3.841. Since the Chi-Square for this problem is 11.6129, seeing it is higher than 3.841, the results would be considered significant.

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