Can you help me with question f, g, h i ? Thank you so much! A teacher did a pol
ID: 3317235 • Letter: C
Question
Can you help me with question f, g, h i ? Thank you so much!
A teacher did a poll of the students attending Happy Valley School as to whether the student believed in Santa Claus or not. The results of the poll are summarized in the table below. 4. Believe in Santa Claus GRADE in School Kindergarten 1st Grade 2nd Grade 3rd Grade 4th Grade 5th Grade TOTAL YES 27 27 19 NO TOTAL 2 9 15 31 6 30 78 186 a) b) c) d) e) Fill in the missing values in the table. (3 points) A student is randomly chosen from the sample; what is the probability that the student does not believe in Santa Claus? Is this a joint, marginal, or conditional probability? (3 points) If a second grader is chosen, what is the probability that he/she believes in Santa? Is this a joint, marginal, or conditional probability? (3 points) What is the probability that a randomly chosen student is in 3rd grade and does not believe in Santa? Is this a marginal, joint or conditional probability? Write out the hypotheses for the Chi-Square(2) test of this data Finish the table of expected counts f)Explanation / Answer
Part a
Completed table is given as below:
Believe in Santa Claus
Grade
Yes
No
Total
Kindergarten
27
2
29
1st
27
6
33
2nd
19
9
28
3rd
16
15
31
4th
13
22
35
5th
6
24
30
Total
108
78
186
Part b
Number of students does not believe in Santa Claus = 78
Total number of students = 186
Required probability = 78/186 = 0.419355
This is a marginal probability.
Part c
Number of students in second grade = 28
Total number of students = 186
Number of 2nd grade students believe in Santa Claus = 19
Required probability = (19/186) / (28/186) = 19/28 = 0.678571
This is a conditional probability.
Part d
Total number of students = 186
Number of students in 3rd grade who does not believe in Santa = 15
Required probability = 15/186 = 0.080645
This is a joint probability.
Part f
We are given a observed frequencies table as below:
Observed Frequencies
Column variable
Yes
No
Total
Kindergarten
27
2
29
1st
27
6
33
2nd
19
9
28
3rd
16
15
31
4th
13
22
35
5th
6
24
30
Total
108
78
186
Now, we have to find expected frequencies. Formula for expected frequencies is given as below:
E = Row total * Column total / Grand total
We are given grand total = 186
By using this formula, table for expected frequencies is given as below:
Expected Frequencies
Column variable
Yes
No
Total
Kindergarten
16.83871
12.16129
29
1st
19.16129
13.83871
33
2nd
16.25806
11.74194
28
3rd
18
13
31
4th
20.32258
14.67742
35
5th
17.41935
12.58065
30
Total
108
78
186
Part g
Formula for partial Chi square values is given as below:
Partial chi square = [(O – E)^2/E)
Where, O is observed frequencies and E is expected frequencies.
Table for partial Chi square is given as below:
Grade
Yes
No
Kindergarten
6.131813
8.490203
1st
3.206745
4.440108
2nd
0.46243
0.640287
3rd
0.222222
0.307692
4th
2.638454
3.653244
5th
7.486022
10.36526
Part h
Chi square test statistic = [(O – E)^2/E) = 48.04448
Number of rows = r = 6
Number of columns = c = 2
Degrees of freedom = (r – 1)*(c – 1) = (6 – 1)*(2 – 1) = 5*1 = 5
Part i
= 0.05
P-value = 0.00 (By using Chi square table or excel)
P-value < = 0.05
So, we reject the null hypothesis that grade and believe in Santa Claus are independent of each other.
There is insufficient evidence to conclude that grade and believe in Santa Claus are independent of each other.
Believe in Santa Claus
Grade
Yes
No
Total
Kindergarten
27
2
29
1st
27
6
33
2nd
19
9
28
3rd
16
15
31
4th
13
22
35
5th
6
24
30
Total
108
78
186
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