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Question 309:



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For a sample this small we'd need to observe large deviations from the mean before we could conclude the difference isn't just chance variation. We'll use the t-statistic and perform a 1-sample t-test on the hypothesized mean of 14 ounces.  The mean  of the data-points is 14.05 and standard deviation is .3464.

The test statistic is derived by subtracting (14.05-14) and dividing by the standard error of the mean. The standard error of the mean is the standard deviation divided by the square root of the sample size minus 1. So the SEM is .3464/SQRT(8) =  .1224. So the t-statistic is 14.05-14)/.1224  = .408 which is the test statistic.

To get the p-value you can look-up .408 using Excel using the formula =TDIST(0.40826,8,2) which provides us with a p-value of about .69, which is no-where near .01, so given the small sample of 8 we are not even close to rejecting the claim that their cereal has a mean of 14oz.

See also question 289

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