Question

A manager wishes to see if the time (in minutes) it takes for their workers to complete a certain task will change when they are allowed to wear ear buds to listen to music at work.
A random sample of 9 workers' times were collected before and after wearing ear buds. Assume the data is normally distributed.
Perform a Matched-Pairs hypotheis T-test for the claim that the time to complete the task has changed at a significance level of α=0.01α=0.01.
(If you wish to copy this data to a spreadsheet or StatCrunch, you may find it useful to first copy it to Notepad, in order to remove any formatting.)
Round answers to 3 decimal places.

For this problem, μd=μAfterμd=μAfter - μμ_Before,
where the first data set represents "after" and the second data set represents "before".
      Ho:μd=0Ho:μd=0
      Ha:μd≠0Ha:μd≠0

This is the sample data:

Before	After
57.7	53.8
74.7	69.5
59.8	56.1
61.8	61.5
52.9	56.7
54	51.1
34.7	24.3
39.9	37.6
54.3	54.7

What is the mean difference for this sample?  
Mean difference (¯dd¯) =


What is the standard deviation difference for this sample?  
standard deviation difference ( sdsd) =

What is the test statistic for this test?  
test statistic =

This P-value leads to a decision to... Select an answer reject the null reject the claim fail to reject the null accept the null  

As such, the final conclusion is that... Select an answer There is sufficient evidence to support the claim that the time to complete the task has changed. There is not sufficient evidence to support the claim that the time to complete the task has changed

Answer 1

Sample #1	Sample #2	difference , Di =sample1-sample2	(Di - Dbar)²
57.7	23.8	33.90	775.31
74.7	69.5	5.20	0.73
59.8	56.1	3.70	5.55
61.8	61.5	0.30	33.13
52.9	56.7	-3.80	97.13
54	51.1	2.90	9.96
34.7	24.3	10.40	18.87
39.9	37.6	2.30	14.10
54.3	54.7	-0.40	41.67

	sample 1	sample 2	Di	(Di - Dbar)²
sum =	489.8	435.3	54.500	996.462

Ho :   µd=   0                  
Ha :   µd ╪   0                  
                          
Level of Significance ,    α =    0.01       claim:µd=0          
                          
sample size ,    n =    9                  
                          
mean of sample 1,    x̅1=   54.422                  
                          
mean of sample 2,    x̅2=   48.367                  
                          
mean of difference ,    D̅ =ΣDi / n =   6.056                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    11.1605                  
                          
std error , SE = Sd / √n =    11.1605   / √   9   =   3.7202      
                          
t-statistic = (D̅ - µd)/SE = (   6.055555556   -   0   ) /    3.7202   =   1.628
                          
Degree of freedom, DF=   n - 1 =    8                     
                          
p-value =        0.1422 [excel function: =t.dist.2t(t-stat,df) ]               
Conclusion:     p-value>α , Do not reject null hypothesis      

. There is not sufficient evidence to support the claim that the time to complete the task has changed               
................

THANKS

revert back for doubt

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