The following figures represent amounts of time in seconds a

The following figures represent amounts of time (in seconds) a random sample of students from this class spent watching the videos for chapter 8. At = 0.01, us this data to test the claim that the average time spent was less than the total run time of the videos (total run time = 435 seconds)

608 610 408 404 516 500

9 947 624 2 514 495

940 501 251 536 700 435

28 0 713 233 4 5

540 511 188 352 486 201

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   435  
Ha:    u   <   435  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha =    0.01          
zcrit =    -   2.326347874      
              
Getting the test statistic, as              
              
X = sample mean =    408.7          
uo = hypothesized mean =    435          
n = sample size =    30          
s = standard deviation =    268.3469383          
              
Thus, z = (X - uo) * sqrt(n) / s =    -0.536808929          
              
Also, the p value is              
              
p =    0.295699802          
              
aS Z > -2.326, and P > 0.01, we   FAIL TO REJECT THE NULL HYPOTHESIS.          

Thus, there is no significant evidence that the average time spent was less than the total run time of the videos (total run time = 435 seconds) at 0.01 level. [CONCLUSION]

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Hi! Some of the data are single digit, which is unusual. If those are typo errors, please resubmit the correct version fo this question. Otherwise, I used the data you submitted. Thanks!