Question

A local brewery distributes beer in bottles labeled 24 ounces. A government agency thinks that the brewery is cheating its customers. The agency selects 50 of these bottles, measures their contents, and obtains a sample mean of 23.7 ounces and sample standard deviation of 0.8 ounces. . Test the claim by the government agency that the population mean is less than 24 ounces at the 0.01 level of significance.

Answer 1

We reject H₀ . We support the feeling of people from a government agency

Explanation:

Population information:

Population mean μ = 24 ou

Sample information:

Sample size n = 50 then degree of fredom df = n - 1 = 49

Sample mean x = 23,7

Sample standard deviation s = 0,8

Hypothesis Test:

Null Hypothesis H₀ x = μ

Alternative hypothesis Hₐ x < μ

Significance level α = 0,01

We can conclude from the alternative hypothesis that we should develop a one tail-test ( to the left " if a local brewery is cheating its customers that mean, they are selling less beer than they are supposed to)

With α = 0,01 and df = 49 we get from t-student table t(c) = - 2,4

To calculate t(s)

t(s) = ( x - μ ) / s/√n

t(s) = ( 23,7 - 24 ) / 0,8/√50

t(s) = - 0,3* 7,07 / 0,8

t(s) = - 2,12 / 0,8

t(s) = - 2,65

Comparing t(c) and t(s)

|t(c)| < |t(s)|

2,4 < 2,65

Then t(s) is in the rejection region we reject H₀ , and agree with a government agency in the fact that at 99 % of confidence interval shows that local brewery is cheating customers