Question

School Enrollment. Refer to Exercise 12:48. For students below postsecondary, solve the following problems.

a. Determine the conditional distribution of level for each gender.

b. Determine the marginal distribution of level.

c. Are the variables "gender"" and "level" associated? Explain your answer

d. Find the percentage of students in nursery school.

e. Find the percentage of females in nursery school.

f. Without doing any further calculations, respond true or false to the following statement and explain your answer: "The conditional distributions of gender within levels are not identical " .

g. Determine and interpret the marginal distribution of gender and the conditional distributions of gender within levels.

Short answer

A )

Level	Male	Female
Nursery	0.079	0.084
Kindergarten	0.073	0.071
Elementary	0.562	0.559
High school	0.286	0.286
Total	1	1

B )

Level	Male	Female	marginal distribution
Nursery	2331	2377	0.082
Kindergarten	2135	1997	0.072
Elementary	16504	15734	0.560
High school	8393	8053	0.286
Total	29363	28161	1

C ) Yes, variables "gender" and "level" are associated because the conditional distribution of gender within levels is not the same.

D ) From part b, the percentage of students in nursery school is $\boxed{8.2\%}$

E ) From part b, the percentage of females in nursery school is $\boxed{8.4\%}$

F ) Here, the given statement is true because the variables "gender" and "level" are associated. This means that the conditional distribution of gender within levels is not the same.

G )

Level	Male	Female	Total
Nursery	0.495	0.505	1
Kindergarten	0.517	0.483	1
Elementary	0.512	0.488	1
High school	0.510	0.490	1
Total	0.510	0.490	1

Step-by-step solution

Step 1. Part ( a ) 

Determine the conditional distribution of level for each gender .

Level	Male	Female
Nursery	0.079	0.084
Kindergarten	0.073	0.071
Elementary	0.562	0.559
High school	0.286	0.286
Total	1	1

Step 2. Part ( b ) 

Determine the marginal distribution of each level .

Level	Male	Female	marginal distribution
Nursery	2331	2377	0.082
Kindergarten	2135	1997	0.072
Elementary	16504	15734	0.560
High school	8393	8053	0.286
Total	29363	28161	1

Step 3. Part ( c ) 

Check whether the variables "sex" and "level" are related or not.

Yes, variables "gender" and "level" are associated because the conditional distribution of gender within levels is not the same.

Step 4. Part ( d ) 

Find the percentage of students in nursery school.

From part b, the percentage of students in nursery school is$\boxed{8.2\%}$

Step 5. Part ( e ) 

Find the percentage of females in nursery school.

From part b, the percentage of females in nursery school is$\boxed{8.4\%}$

Step 6. Part ( f ) 

Check that the statement provided is true or false,

Here, the given statement is true because the variables "gender" and "level" are associated. This means that the conditional distribution of gender within levels is not the same.

Step 7. Part ( g ) 

Determine the marginal distribution of gender and the conditional distributions of gender within levels .

Level	Male	Female	Total
Nursery	0.495	0.505	1
Kindergarten	0.517	0.483	1
Elementary	0.512	0.488	1
High school	0.510	0.490	1
Total	0.510	0.490	1

From the table, it is observed that the conditional distributions of gender within levels are not similar Moreover, the percentage of male within kindergarten level is larger when compared to other level and also the percentage of female within kindergarten level is smaller than the other levels.