A random sample of students at a college reported what they

A random sample of students at a college reported what they believed to be their heights in inches. Then the students measured each others\' heights in centimeters, without shoes. The data provided are for the men, with their believed heights convened from inches to centimeters. Assume that conditions for t-tests hold. Complete pans a and b below. Click the icon to view the data. a. Find a 95% confidence interval for the mean difference as measured in centimeters. Does is capture 0? What does that show? The 95% confidence interval is

Solution

Consider the table:

Calculating the standard deviation of the differences (third column):              
              
s =    3.237304581          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    0.835868449          

For the   0.95   confidence level,      
              
alpha/2 = (1 - confidence level)/2 =    0.025       As df = n - 1 =    14          

t(alpha/2) =    2.144786688          
              
lower bound = [X1 - X2] - t(alpha/2) * sD =    -2.387426188          
upper bound = [X1 - X2] + t(alpha/2) * sD =    1.198092855          
              
Thus, the confidence interval is              
              
(   -2.387426188   ,   1.198092855   ) [ANSWER]

If the order has to be the other way around, then please answer (-1.198, 2.387).

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YES, IT INCLUDES 0, AS YOU CAN SEE.

165.1	168	2.9
170.18	173	2.82
185.42	183	-2.42
172.72	164	-8.72
190.5	189	-1.5
170.18	171	0.82
177.8	174	-3.8
190.5	193	2.5
177.8	177	-0.8
177.8	178	0.2
182.88	181	-1.88
177.8	176	-1.8
167.64	170	2.36
172.72	170	-2.72
182.88	186	3.12