riting a paper on has school -ngsd children and if thhet voher supports reducing
ID: 3317293 • Letter: R
Question
riting a paper on has school -ngsd children and if thhet voher supports reducing the oample of sizs 200, the fullowing table was constructed wards f on a random The responses are Has School-aged Dos not have Children -whool agedChildren. Supports reducing the School budget 40 50 Does not support reducing the School budget 70 40 Test at = .05, if opinion about the school budget is independent of whether a voter has children or not If a researcher needs to reduce both the probability of a type I error and the probability of a type II error the researcher must Bonus (+2 pts). a. b. c. d. reduce the level of confidence increase the level of significance increase the sample size reduce the sample standard deviationExplanation / Answer
Solution:
Here, we have to use Chi square test for independence of two categorical variables. The null and alternative hypotheses for this test are given as below:
Null hypothesis: H0: The school budget is independent of whether a voter has a children or not.
Alternative hypothesis: Ha: The school budget is not independent of whether a voter has a children or not.
The level of significance for this test is given as = 0.05.
The test statistic formula for this test is given as below:
Chi square = [(O – E)^2/E]
Where O is observed frequencies and E is expected frequencies.
Expected frequencies are calculated as below:
Expected frequencies = E = Row total * Column total / Grand total
Tables for observed frequencies, Expected frequencies, and calculations are given as below:
Chi-Square Test
Observed Frequencies
Column variable
Row variable
Has School aged children
Does not have school aged children
Total
Support reducing school budget
40
50
90
Does not support reducing school budget
70
40
110
Total
110
90
200
Expected Frequencies
Column variable
Row variable
Has School aged children
Does not have school aged children
Total
Support reducing school budget
49.5
40.5
90
Does not support reducing school budget
60.5
49.5
110
Total
110
90
200
(O - E)^2/E
1.823232
2.228395
1.491736
1.823232
Number of rows = r = 2
Number of columns = c = 2
df = (r – 1)*(c – 1) = (2 – 1)*(2 – 1) = 1*1 = 1
Critical value = 3.841459149
(By using Chi square table)
Chi square test statistic = [(O – E)^2/E] = 7.366595245
P-value = 0.006644663
(By using Chi square table or excel)
P-value < = 0.05.
So, we reject the null hypothesis that the school budget is independent of whether a voter has children or not.
There is insufficient evidence to conclude that the school budget is independent of whether a voter has children or not.
Chi-Square Test
Observed Frequencies
Column variable
Row variable
Has School aged children
Does not have school aged children
Total
Support reducing school budget
40
50
90
Does not support reducing school budget
70
40
110
Total
110
90
200
Expected Frequencies
Column variable
Row variable
Has School aged children
Does not have school aged children
Total
Support reducing school budget
49.5
40.5
90
Does not support reducing school budget
60.5
49.5
110
Total
110
90
200
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