Do the bakery's loaves really average 800 g?

Question

A bakery advertises that its sourdough loaves average 800 g. A food inspector weighs a random sample of 10 loaves and finds a sample mean of 788 g with a sample standard deviation of 15 g. The population standard deviation is unknown.

Test at the 5% level (two-sided) whether the true mean weight differs from 800 g, and report the t-statistic.

Accepted Answer

The population standard deviation is unknown and the sample is small, so use a one-sample t-test with n - 1 = 9 degrees of freedom. Hypotheses: H0: \mu = 800 versus H1: \mu 
eq 800. Standard error (using the sample standard deviation s): 	ext{SE} = \frac{s}{\sqrt{n}} = \frac{15}{\sqrt{10}} = \frac{15}{3.162} = 4.743 	ext{ g}. Test statistic: t = \frac{\bar x - \mu0}{	ext{SE}} = \frac{788 - 800}{4.743} = \frac{-12}{4.743} = -2.53. The two-sided 5% critical value for 9 degrees of freedom is t{0.025,\,9} = 2.262. Since -2.53 = 2.53 2.262, reject H0. The two-sided p-value is about 0.032. Conc…

Do the bakery's loaves really average 800 g?

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