Statistics Worksheet
Part A
Question 1
a) Below is the calculation for the Pearson product-moment correlation coefficient between the total number of problems correct and the attitude toward test taking. Total no. of problems correct (out of a possible 20): X Attitude toward test taking (out of a possible 100): Y (X - X ̅)² (Y - Y ̅)² (X-X ̅)(Y-Y ̅)
1 17 94 1.96 204.49 20.02
2 13 73 6.76 44.89 17.42
3 12 59 12.96 428.49 74.52
4 15 80 0.36 0.09 -0.18
5 16 93 0.16 176.89 5.32
6 14 85 2.56 28.09 -8.48
7 16 66 0.16 187.69 -5.48
8 16 79 0.16 0.49 -0.28
9 18 77 5.76 7.29 -6.48
10 19 91 11.56 127.69 38.42
Total 156 797 42.40 1206.10 134.80
X ̅=156/10=15.6
Y ̅=797/10=79.7 r=(∑▒〖(X-X ̅)(Y-Y ̅ 〗) )/√(∑▒〖(X-X ̅ )^2 ∑▒(Y-Y ̅ )^2 〗) r=(134.80 )/√(42.40×1206.10)=0.5961 …show more content…
Also, the critical correlation value for the two-tailed test with 48 degrees of freedom is 0.2732. In this case, the calculated correlation statistic exceeds both the critical correlation values at the 0.05 level; therefore, the null hypothesis of no significant correlation is rejected. This implies that there is a moderate positive correlation between the number of friends and GPA for adolescents.
Question 7
a) The correlation between income and level of education is r = .629 (using IBM SPSS).
b) The correlation is highly significant at the 0.01 level, p = .003.
c) The income level has a strong positive correlation with the level of education. However, this should not imply causation between the level of education and income.
Question 8
a) The table below shows the calculation for the correlation coefficient between the age in months and number of words known. Age in months: X Number of words known: Y (X - X ̅)² (Y - Y ̅)² (X-X ̅)(Y-Y ̅)
1 12 6 10.24 13.69 11.84
2 15 8 0.04 2.89 …show more content…
A scatterplot of a weak positive association, for instance, between the age (in months) and height (in inches) of a baby is shown below. A scatterplot of a weak negative association, for instance, between the price of sugar and number of purchases is shown below. The coefficient of determination is the amount of variation in the dependent variable that is explained by the independent variables in a regression model. It is important to know the amount of shared variance when interpreting both the significance and the meaningfulness of a correlation coefficient in order to determine whether the predictors are useful in the model.
In order to predict how well a student might do in college, a researcher might examine various variables, including SAT scores, age, gender, race, and socioeconomic status. In this regard, she might use regression analysis.
The p value of a correlation coefficient is the probability value of obtaining an extreme correlation value or rejecting the null hypothesis that there is no correlation when the hypothesis is
Part A
Question 1
a) Below is the calculation for the Pearson product-moment correlation coefficient between the total number of problems correct and the attitude toward test taking. Total no. of problems correct (out of a possible 20): X Attitude toward test taking (out of a possible 100): Y (X - X ̅)² (Y - Y ̅)² (X-X ̅)(Y-Y ̅)
1 17 94 1.96 204.49 20.02
2 13 73 6.76 44.89 17.42
3 12 59 12.96 428.49 74.52
4 15 80 0.36 0.09 -0.18
5 16 93 0.16 176.89 5.32
6 14 85 2.56 28.09 -8.48
7 16 66 0.16 187.69 -5.48
8 16 79 0.16 0.49 -0.28
9 18 77 5.76 7.29 -6.48
10 19 91 11.56 127.69 38.42
Total 156 797 42.40 1206.10 134.80
X ̅=156/10=15.6
Y ̅=797/10=79.7 r=(∑▒〖(X-X ̅)(Y-Y ̅ 〗) )/√(∑▒〖(X-X ̅ )^2 ∑▒(Y-Y ̅ )^2 〗) r=(134.80 )/√(42.40×1206.10)=0.5961 …show more content…
Also, the critical correlation value for the two-tailed test with 48 degrees of freedom is 0.2732. In this case, the calculated correlation statistic exceeds both the critical correlation values at the 0.05 level; therefore, the null hypothesis of no significant correlation is rejected. This implies that there is a moderate positive correlation between the number of friends and GPA for adolescents.
Question 7
a) The correlation between income and level of education is r = .629 (using IBM SPSS).
b) The correlation is highly significant at the 0.01 level, p = .003.
c) The income level has a strong positive correlation with the level of education. However, this should not imply causation between the level of education and income.
Question 8
a) The table below shows the calculation for the correlation coefficient between the age in months and number of words known. Age in months: X Number of words known: Y (X - X ̅)² (Y - Y ̅)² (X-X ̅)(Y-Y ̅)
1 12 6 10.24 13.69 11.84
2 15 8 0.04 2.89 …show more content…
A scatterplot of a weak positive association, for instance, between the age (in months) and height (in inches) of a baby is shown below. A scatterplot of a weak negative association, for instance, between the price of sugar and number of purchases is shown below. The coefficient of determination is the amount of variation in the dependent variable that is explained by the independent variables in a regression model. It is important to know the amount of shared variance when interpreting both the significance and the meaningfulness of a correlation coefficient in order to determine whether the predictors are useful in the model.
In order to predict how well a student might do in college, a researcher might examine various variables, including SAT scores, age, gender, race, and socioeconomic status. In this regard, she might use regression analysis.
The p value of a correlation coefficient is the probability value of obtaining an extreme correlation value or rejecting the null hypothesis that there is no correlation when the hypothesis is