Question

Administrators are sure about the effectiveness of the Apple Orchard Preschool spelling program. The average spelling score is 25 for children of comparative age. The data below are spelling scores from a sample of children from Apple Orchard Preschool. Scores range from 0 - 40 with higher scores indicating better spelling. What can be concluded with an α of 0.05?

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

a) What is the appropriate test statistic?
---Select---

Options are: na, z-test, One-Sample t-test, Independent-Samples t-test, or Related-Samples t-test

b)
Population:
---Select---

-Options are: Apple Orchard Preschool, spelling, children of comparative age, spelling scores, or Administrators

Sample:
---Select---

-Options are: Apple Orchard Preschool, spelling, children of comparative age, spelling scores, or 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---

Options are: Reject H0 Fail or 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---

-Options are: na, trivial effect, small effect, medium effect, or large effect

r² = _____ ;   ---Select---

-Options are: na, trivial effect, small effect, medium effect, or large effect

e) Make an interpretation based on the results. Which one is correct?

a)Apple Orchard Preschool has a significantly effective spelling program.

b)Apple Orchard Preschool has a significantly ineffective spelling program.    

c)Apple Orchard Preschool spelling program does not have a significant effect.

Answer 1

Solution:

a)The appropriate test statistic is one sample t-test. Since n< 30, we use t- test.

b)Population: Apple Orchard Preschool children

Sample: Children of comparative age

c) The following table shows the T test result from excel.

t-Test: One sample t test
	spelling
Mean	24.85
Variance	42.34473684
Observations	20
Hypothesized Mean Difference	25
df	19
t Stat	-0.103087626
P(T<=t) one-tail	0.459486863
t Critical one-tail	1.729132812
P(T<=t) two-tail	0.918973726
t Critical two-tail	2.093024054

Hypothesis:

Null Hypothesis H₀: =25

Alternative Hypothesis H₁: 25

P value from the above table= 0.918973726

Since t Stat=-0.103087626 which is less than t Critical value=2.093024054, we accept the null hypothesis and conclude =25.

e) a)Apple Orchard Preschool has a significantly effective spelling program.