SOLUTION: The numbers of people waiting in the emergency clinic of a small health care facility were randomly counted thirty-five times. Using the data below and the appropriate formula, set

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Question 406695: The numbers of people waiting in the emergency clinic of a small health care facility were randomly counted thirty-five times. Using the data below and the appropriate formula, set up a 95% confidence interval for the mean number of people waiting in emergency.
11 12 13 13 14 14 14
15 17 16 16 17 17 16
15 15 18 19 16 16 18
17 17 18 17 16 16 16
15 9 10 18 14 11 9
(where x and s are calculated from the sample data, n = 35 and z = 1.96)
Remember to show all your work and round your final answer to the nearest whole number.

Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!


Hi

entering the data in an Excel Cloumn and used the stat tool found:

 = 2.623423897  and mean = 15



ME = 1.96*2.6234/sqrt(35) = 5.9161		

CI: 15-5.9161 < u < 15+ 5.9161		

 

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
 Find the mean :



11 12 13 13 14 14 14........91

15 17 16 16 17 17 16..........114

15 15 18 19 16 16 18..........117

17 17 18 17 16 16 16..........117

15 9 10 18 14 11 9..................86



......the mean is  





The is





Find the standard deviation of  using this formula first:



subtract the mean individually from each of the numbers in the question and square the result.

x               11       12        13       13       14       14        14        

(x - x)²     16         9           4       4           1         1           1..........36



x               15       17        16       16       17       17        16        

(15 - x)²     0         4           1        4         4         4          1.............18



 x   	    15 	15	18	 19	 16	 16 	18

(15 - x)²     0	 0  	  9	   16        1          1         9.............36





x   	    17 	17	18	 17	 16	 16 	16

(15 - x)²     4	 4  	  9	  4          1          1         1..................24



x   	    15 	 9	10	 18	 14	 11 	9

(15 - x)²     0	 36  	  25	  9          1          16      36............123

----------------------------------------------------------------------------------------------

                                                                                                     237

                                                                                                                    

Now add up these results (this is the 'sigma' in the formula): 237



, 



 



 









the standard deviation is 

	 		









= 15 +-(1.96(2.6401871591412071041056987587526))/sqrt(35)



= 15 +-( 5.1747668319167659240471695671539)=15+-5.18













So the interval is ....in average:14.995







 

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