A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.6; 2.8; 3.1; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)     part a Construct a 95% confidence interval for the population mean length of time. (i) State the confidence interval. (Round your answers to two decimal places.)       (ii) part b Sketch the graph. a/2 =  CL= a/2 =   part c iii) Calculate the error bound. (Round your answer to two decimal places.) Part (d What does it mean to be "95% confident" in this problem? This means that the chances of a tranquilizer being effective is 95%. This means that we are 95% confident that the average length of effectiveness of tranquilizers in the sample of 9 people is between the interval values.     We are 95% confident that the effectiveness of a tranquilizer lies between the interval values. This means that if intervals are created from repeated samples, 95% of them will contain the true population average length of effectiveness of tranquilizers.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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  • A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.6; 2.8; 3.1; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4.
  • NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
  •  
  •  
  • part a Construct a 95% confidence interval for the population mean length of time.
    (i) State the confidence interval. (Round your answers to two decimal places.)

 
  •  
 



(ii) part b Sketch the graph.

a/2 = 

CL=

a/2 =

 

  • part c iii) Calculate the error bound. (Round your answer to two decimal places.)

  • Part (d
    What does it mean to be "95% confident" in this problem?
  • This means that the chances of a tranquilizer being effective is 95%.
  • This means that we are 95% confident that the average length of effectiveness of tranquilizers in the sample of 9 people is between the interval values.    
  • We are 95% confident that the effectiveness of a tranquilizer lies between the interval values.
  • This means that if intervals are created from repeated samples, 95% of them will contain the true population average length of effectiveness of tranquilizers.
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