Question

Administrators want to know the effectiveness of the Orange
Grove Elementary reading program. The average reading comprehension
score is 22 for children of comparative age. The data below are
reading comprehension scores from a sample of children from Orange
Grove Elementary. Scores range from 0 - 40 with higher scores
indicating better reading comprehension. What can be concluded with
α = 0.05?

id |
reading |

35 36 37 38 39 40 41 42 43 44 45 10 11 12 13 14 15 16 17 18 |
27 33 38 17 19 27 29 18 21 35 18 28 23 22 24 20 35 24 17 16 |

**a)** What is the appropriate test statistic?

---Select--- na z-test One-Sample t-test Independent-Samples t-test
Related-Samples t-test

**b)**

Population:

---Select--- reading reading comprehension scores Orange Grove
Elementary children of comparative age Administrators

Sample:

---Select--- reading reading comprehension scores Orange Grove
Elementary children of comparative age Administrators

**c)** Input the appropriate value(s) to make a
decision about *H*_{0}.

(Hint: Make sure to write down the null and alternative hypotheses
to help solve the problem.)

*p*-value = ; Decision: ---Select---
Reject H0 Fail to reject H0

**d)** Using the **SPSS** results,
compute the corresponding effect size(s) and indicate
magnitude(s).

If not appropriate, input and/or select "na" below.

*d* = ; ---Select--- na trivial
effect small effect medium effect large effect

*r*^{2} = ; ---Select--- na
trivial effect small effect medium effect large effect

**e)** Make an interpretation based on the
results.

Orange Grove Elementary has a significantly effective reading program.Orange Grove Elementary has a significantly ineffective reading program. Orange Grove Elementary reading program does not have a significant effect.

Answer #1

*Soln*

a)

One Sample t test

b)

Population: Orange Grove Elementary children of comparative age

Sample: Orange Grove Elementary children of comparative age
Administrators

c)

From the data, we calculate the mean and standard deviation.

Mean (X) = Sum of Values /n = 24.55

and

Std Dev(s) = 6.73

n = 20

*Null and Alternate
Hypothesis*

H_{0}: µ = 22

H_{a}: µ > 22

*Test Statistic*

t = (X- µ_{0})/(s/n^{1/2}) = 1.69

p-value = TDIST(1.69,20-1,1) = 0.053

*Result*

Since the p-value is greater than 0.05, we fail to reject the null hypothesis

*Conclusion*

average reading comprehension score is 22

d)

Effect Size = (X- µ_{0})/s = 0.38

trivial effect small effect

e)

Orange Grove Elementary reading program does not have a significant effect.

Regents are certain about the ineffectiveness of the Orange
Grove Preschool reading program. The average reading comprehension
score is 25 for children of comparative age. The data below are
reading comprehension scores from a sample of children from Orange
Grove Preschool. Scores range from 0 - 40 with higher scores
indicating better reading comprehension. What can be concluded with
α = 0.01?
id
reading
35
36
37
38
39
40
41
42
43
44
45
10
11
12
13
14...

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reading
35
36
37
38
39
40
41
42
43
44
45
10
11
12
13
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