tB 2.E.034 A study of reading ability in schoolchildren chose 60 fith-grade chil
ID: 3045310 • Letter: T
Question
tB 2.E.034 A study of reading ability in schoolchildren chose 60 fith-grade children at random from a school.t The main purpose of this study was to ask estimate their own reading ability. The researchers had the children's scores on a test of reading ability. They asked from 1 (low) to 5 Chigh). The igure shown below is a scatplot of the chidren's estimates (response) each child to estimate his or her reading level, on a scale against their reading scores (explanatory) 0 20 40 60 80 100 Child's score on a test of reading ability (a) What explains the "stair-step" pattern in the plot? O The relationship between the explanatory variable (child's score) and the response O The res variable (estimated level) will always exhibit this pattern. five levels. ponse variable (estimated level) can only take on the values 1, 2, 3, 4, 5, so the points in the scatterplot must fall on one of those Children are very good at estimating their reading ability Many relationships in the real world exhibit this pattern naturally (b) Is there an overall positive association between reading score and self-estimate? The association is (weakly) negative. The associaExplanation / Answer
Solution :
a) Option b is correct.
As we can see in the figure , the response variable only take values 1,2,3,4 and 5, that is it is discrete with these 5 values.So association with a variable which is discrete or not discrete ,it will have possibility of having 0,1,2....100.
and when we find relation between the two, we get more repeated values of response variable and therefore we get "Stair -step" pattern in the graph.
b) the correct option is b.
Here association is positive but extremely weak. If we look at the graph, for the increase in x values , the response variable y is increasing (look at the reading score from 60 onwards ,the values are increasing as compared to the scores of 0 to 40).
c. The outlier is the point very far from the other data values,so here point(12,4) is the outlier. A more common value would have been 3 or less,so this value is an overestimate of the child’s reading ability with respect to the self-estimate .
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