SOLUTION: A food snack manufacturer samples 7 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 14.2 oz. and the sample standard deviation is 0.60 oz.,

Question 1086252: A food snack manufacturer samples 7 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 14.2 oz. and the sample standard deviation is 0.60 oz., find the 95% confidence interval of the true mean.

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
standard error(SE) = 0.60 / square root(7) = 0.2268
:
alpha(a) = 1 - (95/100) = 0.05
critical probability (p*): p* = 1 - α/2 = 1 - 0.05/2 = 0.975
degrees of freedom(df) = 7 - 1 = 6
:
the critical value(CV) is the t statistic with 6 degrees of freedom and a cumulative probability of 0.975. We lookup these values in the t-tables to
find the critical value is 2.447
:
margin of error(ME) = CV * SE = 2.447 * 0.2268 = 0.555
:
confidence interval(CI) = the sample statistic + or - the margin of error
:
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95% CI = 14.2 + or - 0.555, (13.645, 14.755)
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