This Question: 1 pt 3 of 6 (0 complete) This Qu The accompanying table contains

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This Question: 1 pt 3 of 6 (0 complete) This Qu The accompanying table contains two samples that were collected as matched pairs. Complete parts (a) and (b) below. Click the icon to view the data table Click the icon to view a portion of the Student's t-Distribution table a) Construct a 95% confidence interval to estimate the difference in means between the populations from which Sample 1 and 2 were drawn. The difference is defined as Sample 1-Sample 2. UCL LCL (Round to two decimal places as needed.) b) What conclusions can be made based on these results? The interval zero, so there ! enough evidence to conclude that there is a difference in means between the populations from which Sample 1 and 2 were drawn. More Info Pair Sample 1 Sample 2 10 6 9 PrintDone

Explanation / Answer

Here the difference between sample 1 and sample 2 table is

here dbar = -3.5714

standard deviation of difference sd =  3.60

95% confidence interval = dbar +- t1-a, df (sd / sqrt(n) )

{ note : Here dF = 6 and alpha = 0.05 ; t6,0.05 =

LCL (dbar ) = -3.5714 - 2.447 * (3.60/ sqrt(7) = -3.5714 - 3.3296 = -6.90

UCL (dbar ) = -3.5714 + 2.447 * (3.60/sqrt(7) =  -3.5714 +  3.3296 = -0.242

(b) The interval doesn't contain zero, so there is enough evidence that there is a difference in means between the populations.

Pair Sample 1 Sample 2 Difference 1 5 9 -4 2 2 5 -3 3 6 6 0 4 5 10 -5 5 2 9 -7 6 9 7 2 7 1 9 -8 Average -3.5714

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