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 H₀.
(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
r² =  ;   ---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

H₀: µ = 22

H_a: µ > 22

Test Statistic

t = (X- µ₀)/(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- µ₀)/s = 0.38

trivial effect small effect

e)

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