Statistics: Hypothesis Testing, Correlation, Regression

This document covers various topics in statistics including hypothesis testing, correlation, and regression. It explains the process of hypothesis testing and provides an example. It also discusses the concept of correlation and how to interpret correlation coefficients. Additionally, it explains the least square formula and how to use it to predict scores in regression analysis. If you need assistance with statistics assignments or essays, Desklib can help.

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QUESTION 1
Direct Indirect Total
Male 5 10 15
Female 25 10 35
Total 30 20 50
Table 1
a. It is a two tailed test
b. Dependent variable: Choice
c. Independent variable: Sex
d. Hypothesis
H0: Sex and the choice of direct versus indirect social work practice are independent.
H1: Sex and the choice of direct versus indirect social work practice are not independent
e. Degrees of freedom ( r −1 ) ( c−1 )= ( 2−1 ) ( 2−1 )=1
Er ,c= ( nr ×nc ) /n
E1,1 =15 ×30
50 =9
E1,2 =15 ×20
50 =6
E2,1 =35 ×30
50 =21
E2,2 =35 × 20
50 =14
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X2 =∑ [ ( nr ,c−Er , c )2 / Er ,c ]
X2 = ( 5−9 ) 2
9 + ( 10−6 ) 2
6 + ( 25−21 ) 2
21 + ( 10−14 ) 2
14
X2 =1.78+2.67+0.76+1.14=6.35
Using chi-square distribution calculator to find p-value we get;
P ( X2 >6.35 ) =0.01
Since P-value (0.01) is less than the significance level (0.05), we reject the null hypothesis. We
conclude therefore that sex and the choice of direct versus indirect social work practice are not
independent.
QUESTION 2
a. It is a one tailed test
b. Independent variable: Group work
c. Dependent variable: Standardized assertiveness scale.
d. Null hypothesis
H0: There is no significant difference between the mean assertiveness scale score for group work
and individual work.
H1: Mean assertiveness scale score for group work greater than mean assertiveness scale score
for individual work.
Paired sample t-test was employed and the results are as shown below;
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Paired Samples Test
Paired Differences t df Sig. (2-
tailed)Mean Std.
Deviation
Std. Error
Mean
95% Confidence Interval
of the Difference
Lower Upper
Pair 1 group -
individual
23.000
00
11.59502 3.66667 14.70542 31.29458 6.273 9 .000
Table 2
Since P-value (0.00) is less than the significance level (0.05), we reject the null hypothesis. We
conclude therefore that mean assertiveness scale score for group work greater than mean
assertiveness scale score for individual work. Hence group work was more effective in helping
female survivors of abuse than individual work.
NUMBER 3
TEST FOR RELATIONSHIP
Correlations
Maths quiz Stats exam
Maths quiz
Pearson Correlation 1 .889**
Sig. (2-tailed) .001
N 10 10
Stats exam
Pearson Correlation .889** 1
Sig. (2-tailed) .001
N 10 10
**. Correlation is significant at the 0.01 level (2-tailed).
Table 1
Pearson correlation test is used to measure the extent of relationship between two variables. It
measures the relationship both in the positive and negative direction. The range of Pearson
correlation is from -1 to 1. Negative 1 means that there is a very strong relationship between the
two variables but in the negative direction. Positive 1 means that there is a very strong
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relationship between the two variables but in the positive direction. A Pearson correlation of zero
on the other hand indicates that there is no correlation between the two variables.
From table 1 above therefore it can be observed that there is a very strong and positive
relationship between maths quiz and stats exam scores. This is indicated by a Pearson correlation
value of 0.89.
QUESTION 4
1. The least square formula is as shown on the scatterplot below;
5.5 6 6.5 7 7.5 8 8.5 9 9.5
0
10
20
30
40
50
60
70
80
90
100
f(x) = 8.1578947368421 x + 12.3684210526316
R² = 0.790296052631579
Stats Exam vs Math quiz
MATH QUIZ
STAT EXAM
Figure 1
Stat exam =8.16 ( Mathquiz ) +12.37
2. If a student scores 8 in maths quiz what will he score in stats exam?
Stat exam=8.16 ( 8 ) +12.37=77.65
The student will score 77.65 marks
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This is so because the regression equation states that a one unit change in math quiz causes 8.16
units change in stat exam. Therefore if math score changes by 8 units, then stat score will change
to (8 x 8.16) units plus a constant 12.37
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