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Grades on a standardized test are known to have a mean of 10901090 for students in...

Grades on a standardized test are known to have a mean of 10901090 for students in the United States. The test is administered to 458458 randomly selected students in​ Florida; in this​ sample, the mean is 1104.171104.17 and the standard deviation ​(s​) is 117.72117.72. Another 508508 students are selected at random from Florida. They are given a​ 3-hour preparation course before the test is administered. Their average test score is 1110.711110.71 with a standard deviation of 103.55103.55. The​ 95% confidence interval for the change in average test score associated with the prep course is ​(1101.711101.71​, 1119.711119.71​). ​(Round your responses to two decimal

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for prep course data is

Level of Significance ,    α =    0.05
sample std dev ,    s =    103.55
Sample Size ,   n =    508
Sample Mean,    x̅ =   1110.71

degree of freedom=   DF=n-1=   507  
't value='   tα/2=   1.9647   [Excel formula =t.inv(α/2,df) ]
          
Standard Error , SE =   s/√n =   4.5943  
margin of error ,   E=t*SE =   9.0262  
confidence interval is           
Interval Lower Limit=   x̅ - E =    1101.68  
Interval Upper Limit=   x̅ + E =    1119.74

  
The​ 95% confidence interval for the change in average test score associated with the prep course is (1101.68,1119.74)

orchestra answered 2 years ago
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