1 The contents of jars of honey may be assumed to be normally distributed. The contents, in grams, of a random sample of 8 jars were as follows:
458, 450, 457, 456, 460, 459, 458, 456
a) Calculate a 95% confidence interval for the mean contents of all jars:
x̅ = 456.75 Sx: 3.059 n = 8 ν = 7
using calculator: Multiplier = 2.365
95% CI = 456.75 +- 2.365 x (3.059)/root(8)
= (454.192, 459.308).
b) On each jar it states `contents 454 grams.' Comment on this statement using the given sample and your results to part a):
Evidence from part a) shows that the mean is above 454g, but some jars will contain less.
c) Given that the mean contents of all jars is 454 grams, state the probability that a 95% confidence interval calculated from the contents of a random sample of jars will not contain 454 grams.:
I know the probability is 0.05, but my question is why? Surely the probability of a jar content not lying in the confidence interval calculated in part (a) is 0.05 right? So why is the probability that X doesn't equal 454 0.05??