Question

district	percentage working class	unemployment rate	voter turnout
1	50	10	56
2	45	12	55
3	56	8	52
4	78	15	60
5	13	5	89
6	85	20	25
7	62	18	64
8	33	9	88
9	25	0	42
10	49	9	36

The following data was collected for a random sample of 10 electoral districts during the last federal election. The first variable reports the percentage of individuals in each district who belong to the working class; the second variable reports the percentage of individuals who are unemployed; and the third variable reports the percentage of eligible individuals (i.e., citizens at least 18 years old) who voted in the last federal election.

35. Find the mean and standard deviation of each of the three variables. Round to 2 decimal places.

    A) (i) Percentage working-class B) (ii) Unemployment rate C) (iii) Voter turnout

36. How would you describe the distribution of the variable percentage working-class?

    (a) Approximately bell-shaped or symmetric or Normal (b) Left (or negatively) skewed (c) Right (or positively) skewed) (d) Too little information to tell

37. Calculate the correlation between each pair of variables. Round to 2 decimal places.

    a) (i) Percentage working-class & unemployment rate b) (ii) Percentage working-class & voter turnout c) (iii) Unemployment rate & voter turnout

38. Calculate the appropriate test statistic for each correlation. Round to 2 decimal places.

    a) (i) Percentage working-class & unemployment rate b) (ii) Percentage working-class & voter turnout c (iii) Unemployment rate & voter turnout

39. Find the critical value of t (α = .05) for each correlation.

    a) (i) Percentage working-class & unemployment rate b) (ii) Percentage working-class & voter turnout c) (iii) Unemployment rate & voter turnout

40. setting your level of significance at α = .05, for which pairs of variables did you find a statistically significant relationship? Choose all that apply.

    (a) Percentage working-class & unemployment rate (b) Percentage working-class & voter turnout (c) Unemployment rate & voter turnout
    (d) None of the pairs are significantly related to one another.

Answer 1

for percentage working class

	X	(X - X̄)²
total sum	496	4496.40
n	10	10

mean =    ΣX/n =    496.000   /   10   =   49.60
                            
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (4496.4/9)   =       22.35
...................

for unemployment rate

	X	(X - X̄)²
total sum	106	320.40
n	10	10

mean =    ΣX/n =    106.000   /   10   =   10.60       
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (320.4/9)   =       5.97

....................

for voter turnout

	X	(X - X̄)²
total sum	567	3762.10
n	10	10

mean =    ΣX/n =    567.000   /   10   =   56.70    
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (3762.1/9)   =       20.45

.......................

for percentage working class:   almost bell shaped

for unemployment rate: skewed to left

for voter turnout : skewed to right

..........................

for percentage working class and unemployment rate

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	496	106	4496.4	320.4	1019.40
mean	49.60	10.60	SSxx	SSyy	SSxy

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.8493
correlation hypothesis test              
Ho:   ρ = 0       tail=   2
Ha:   ρ ╪ 0          
n=   10          
alpha,α =    0.05          
correlation , r=   0.8493          
t-test statistic = r*√(n-2)/√(1-r²) =        4.551  

critical t-value =    2.3060     
DF=n-2 =   8          
  
Decison:   test stat >critical , So, Reject Ho          

........................

for percentage working class and voter turnout

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	496	567	4496.4	3762.1	-2288.20
mean	49.60	56.70	SSxx	SSyy	SSxy

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   -0.5563  
correlation hypothesis test              
Ho:   ρ = 0       tail=   2
Ha:   ρ ╪ 0          
n=   10          
alpha,α =    0.05          
correlation , r=   -0.5563          
t-test statistic = r*√(n-2)/√(1-r²) =        -1.894  

critical t-value =    2.3060           
DF=n-2 =   8          
Decison:   critical value > test stat, So, Do not reject Ho  

..................

for unemployment rate and voter turnout

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	106	567	320.4	3762.1	-261.20
mean	10.60	56.70	SSxx	SSyy	SSxy

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   -0.2379
correlation hypothesis test              
Ho:   ρ = 0       tail=   2
Ha:   ρ ╪ 0          
n=   10          
alpha,α =    0.05          
correlation , r=   -0.2379          
t-test statistic = r*√(n-2)/√(1-r²) =        -0.693  

critical t-value =    2.3060               
DF=n-2 =   8          
  
Decison:   test stat < critical value, So, Do not reject Ho

.....................

this pair has statistically significant relationship

(a) Percentage working-class & unemployment rate

       

..............................

Please revert back in case of any doubt.

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