Question

A bottled water distributor wants to determine whether the mean amount of water contained
in 1-gallon bottles purchased from a nationally known water bottling company is actually 1
gallon. You know from the water bottling company specifications that the standard deviation of
the amount of water per bottle is 0.02 gallon. You select a random sample of 50 bottles, and
the mean amount of water per 1-gallon bottle is 0.995 gallon.
(a) Is there evidence that the mean amount is different from 1.0 gallon? (Use α = 0.01)
(b) Compute the p-value and interpret its meaning.

Answer 1

given data are:-

sample mean () = 0.995

population sd () = 0.02

sample size(n) = 50

here, as the population sd is known we will do 1 sample Z test for mean.

a).hypothesis:-

where, is the true mean amount of water contained in 1-gallon bottles .

the test statistic be:-

z critical value for 99% confidence level, both tailed test be:-

rejection rule:-

reject the null hypothesis if,

decision:-

so, we fail to reject the null hypothesis.

conclusion:-

there is not sufficient evidence to support the claim that the mean amount is different from 1.0 gallon at 0.01 level of significance.

b). p value be:-

[ in any blank cell of excel type =NORMSDIST(-1.768) press enter ]

interpretation:-

p value = 0.0771 > 0.01 (alpha)

so, we fail to reject the null hypothesis. and conclude that there is not sufficient evidence to support the claim that the mean amount is different from 1.0 gallon at 0.01 level of significance.

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