Question

Construct a 95% confidence interval for sample size 25, sample mean 10, and sample standard deviation 6. 

          Construct a 95% confidence interval for sample size 25, sample mean 10, and sample standard deviation 6.

Added by Patricia C.

Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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Construct a 95% confidence interval for sample size 25, sample mean 10, and sample standard deviation 6.
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Transcript

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00:01 Question it says we have been asked to construct a 95 % confidence interval for the population in standard division if a sample size is 10 and the standard deviation is 16 all right so here standard deviation is 16 so the variance will be 256 right now we need to determine two values here that is the square right which is kai square alpha by 2 for the given degrees of freedom now here n is equal to 10 the degrees of freedom will be n minus 1 that is 9 right and alpha here is 0 .05 so the alpha by 2 it will be 0 .025 right now here the value of pi square 0 .025 so the given degrees of freedom that is 9 it is equal to 19 .023 and the kai square left value will be kai square one minus alpha by two degrees of shriton that is one minus 0 .025 right so that is equal to 0 .975 right so we have to determine the value of kai square 0 .97594 which is 2 .7000 so 95 % confidence interval will be so this will be square root n minus 1 and square upon i squared alpha by 2 and this and n minus 1 square upon okay square 1 minus alpha by 2 right so this will be equal to 5 root of 9 multiplied by 266 .19 .0239 into 256 upon 2 .70.
02:28 So when we solve this, it will be 11 .01.
02:32 This is then 29 .21...
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