intro statistics homework

1.  Reading readiness of preschoolers from an impoverished neighborhood (n = 20) was measured using a standardized test.  Nationally, the mean on this test for preschoolers is 30.9, with SD = 2.08.

 

 

 

 

 

 

 

 

 

 

a.  Children below the 30^th percentile (in the bottom 30%) are in need of special assistance prior to attending school.  What raw score marks the cut-off score for these children? 

 

Z-score =-2.75X = 30.9 + 2.08 (-2.75) = 25.18

                                               

Cut Off is 25.18

 

b.  What percentage of children score between 25 and 28.5?

 

Z= (25-30.9) /2.08= -2.83 Z= (28.5-30.9) /2.08= -1.15

 

-2.83+-1.15=-3.98 50-3.98=46.02

 

 46.02% score between 25 and 28.5

 

c.  How many children would we expect to find with scores between 28 and 31.5?

 

Z= (28-30.9) /2.08= -1.39 Z= (31.5-30.9) /2.08= .28

 

-1.39+. 28= -1.11 Z-score= 2.29

 

X= 30.9 + 2.08 (2.29) = 35.66 

 

36 Children have scores between 28 and 31.5

 

d.   Children in the top 25% are considered accelerated readers and qualify for different placement in school.  What raw score would mark the cutoff for such placement?  

 

Z-score= 2.81X= 30.9 + 2.08(2.81) = 9.74

 

Cut-Off is 9.74

 

2.  Age at onset of dementia was determined for a sample of adults between the ages of 60 and 75.  For 15 subjects, the results were ΣX = 1008, and Σ (X-M)² = 140.4.  Use this information to answer the following:           

 

 

 

 

 

 

 

 

 

 

 

a.  What is the mean and SD for this data

 

M = 1008 /15            M = 67.2            SD= 140.4

b.  Based on the data you have and the Normal Curve Tables, what percentage of people might start to show signs of dementia at or before age 62?

(62-67.2)

      0.037

c.  If we consider the normal range of onset in this population to be +/-1

Z-score from the mean, what two ages correspond to this?

           

 

 

 

d.  A neuropsychologist is interested only in studying the most deviant portion of this population, that is, those individuals who fall within the top 10% and the bottom 10% of the distribution. She must determine the ages that mark these boundaries. What are these ages?