Question

A cognitive psychologist working in the area of suggestion asked a sample of children to solve as many problems as they could in 10 minutes. Half of the children are told that this is a problem-solving task and the other half are told that this is just a time-filling task. The psychologist hypothesizes that thinking it is a problem-solving task will improve problem solving. What can be concluded with an α of 0.05? Below is the data for the number of problems solved.

problem-solving	time-filling
3 4 5 4 2 6 4	10 5 8 7 6 8 7

a) What is the appropriate test statistic?
---Select--- na z-test One-Sample t-test Independent-Samples t-test Related-Samples t-test

b.Condition 1:
---Select--- suggestion the children problems solved problem-solving time-filling
Condition 2:
---Select--- suggestion the children problems solved problem-solving time-filling

c) Obtain/compute the appropriate values to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[  ,  ]

e) 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

f) Make an interpretation based on the results.

Children that were told this is a problem-solving task solved significantly more problems than children that were told this is a time-filling task.Children that were told this is a problem-solving task solved significantly less problems than children that were told this is a time-filling task.     The suggestions had no significant impact on problem solving.

Answer 1

Answer:-

Given That:-

A cognitive psychologist working in the area of suggestion asked a sample of children to solve as many problems as they could in 10 minutes. Half of the children are told that this is a problem-solving task and the other half are told that this is just a time-filling task

a) What is the appropriate test statistic?
---Select--- na z-test One-Sample t-test Independent-Samples t-test Related-Samples t-test

Independent-Samples t-test

b.Condition 1:
---Select--- suggestion the children problems solved problem-solving time-filling
Condition 2:
---Select--- suggestion the children problems solved problem-solving time-filling

condition 1 : problem solving

condition 2: time filling

c) Obtain/compute the appropriate values to make a decision about H0.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

Sample #1 ----> 1
mean of sample 1,

x̅1= 4.286
standard deviation of sample 1, s1 = 1.704
size of sample 1, n1= 7
  
Sample #2 ----> 2
mean of sample 2,

x̅2= 7.286
standard deviation of sample 2, s2 = 1.604
size of sample 2, n2= 7
  
difference in sample means = x̅1-x̅2

= 4.2857 - 7.3

= -3.00
  
pooled std dev , Sp=

= 1.6547
std error , SE =

   = 0.8845
  
t-statistic = ((x̅1-x̅2)-µd)/SE)

= ( -3.0000 - 0) / 0.88

= -3.3918
  
Degree of freedom, DF= n1+n2-2

= 12
t-critical value , t* = 2.179 (excel formula =t.inv(α/2,df)

decision: Reject Ho

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[  ,  ]

Degree of freedom, DF= n1+n2-2

= 12
t-critical value = t α/2 = 2.1788 (excel formula =t.inv(α/2,df)
  
pooled std dev , Sp=

= 1.6547
  
std error , SE =

= 0.8845
margin of error, E = t*SE

= 2.1788 * 0.88

=1.93
  
difference of means = x̅1-x̅2

= 4.2857 - 7.286

= -3.0000
confidence interval is   
Interval Lower Limit= (x̅1-x̅2) - E

= -3.0000 - 1.9271

= -4.927
Interval Upper Limit= (x̅1-x̅2) + E

= -3.0000 + 1.9271

= -1.073

e) 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

effect size,
cohen's d = |(x̅1-x̅2 )/Sp |

= 1.8130 (large)
  
r²= 0.489 (large)

f) Make an interpretation based on the results. Children that were told this is a problem-solving task solved significantly more problems than children that were told this is a time-filling task.Children that were told this is a problem-solving task solved significantly less problems than children that were told this is a time-filling task.     The suggestions had no significant impact on problem solving.

Children that were told this is a problem-solving task solved significantly less problems than children that were told this is a time-filling task.

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