Question

Chancellors are sure about the ineffectiveness of the Apple Orchard Preschool reading program. The average reading comprehension score is 29 for children of comparative age. The data below are reading comprehension scores from a sample of children from Apple Orchard Preschool. 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 22 22 24 20 35 24 17 16

a) What is the appropriate test statistic?
---Select---na, z-tes, tOne-Sample t-test, Independent-Samples t-test, related-Samples t-test

b)
Population:
---Select---reading comprehension scores, Apple Orchard Preschool, children of comparative age, Chancellors, reading
Sample:
---Select---reading comprehension scores, Apple Orchard Preschool, children of comparative age, Chancellors, reading

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 or 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.

Apple Orchard Preschool has a significantly effective reading program.

Apple Orchard Preschool has a significantly ineffective reading program.

    Apple Orchard Preschool reading program does not have a significant effect.

Answer 1

Solution:-

Given that

Chancellors are sure about the ineffectiveness of the Apple Orchard Preschool reading program. The average reading comprehension score is 29 for children of comparative age. The data below are reading comprehension scores from a sample of children from Apple Orchard Preschool. Scores range from 0 - 40 with higher scores indicating better reading comprehension.What can be concluded with α = 0.05?.

a) What is the appropriate test statistic?

One Sample t test

b)
Population:

Population: Apple Orchard Preschool children of comparative age

Sample: Apple Orchard Preschool children of comparative age Chancellors.

c) Input the appropriate value(s) to make a decision about H0.

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 = 29

Ha: µ > 29

Test Statistic

t = (X- µ0)/(s/n1/2) = 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 29.

d) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.

Effect Size = (X- µ0)/s = 0.38

trivial effect small effect

e) Make an interpretation based on the results.

Apple Orchard Preschool reading program does not have a significant effect.

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