Question

a) Identify the claim: state the null and alternative hypotheses. b) Determine the test: left-tailed, right-tailed, or two-tailed. c) Graph your bell-shaped curve and label your levels of significance or critical value. d) Find your standardized test statistic ? and label it on your graph. e) Decide whether to reject or fail to reject the null hypothesis. f) Interpret your result.

A local brewery distributes beer in bottles labeled 32 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 31.7 ounces with a population standard deviation of 0.70 ounce. Use a 0.01 significance level to test the agency's claim that the brewery is cheating its customers.

Answer 1

Given

A local brewery distributes beer in bottles labeled 32 ounces.

a)

null and alternative hypothesis:

H₀: = 32

H₁ : 32

n = 50

sample mean () = 31.7 ounces

standard deviation () = 0.70 ounce

= 0.01 = /2 = 0.005

b)

the test is two-tailed test

c)

df = n-1 = 49

t_critical = t _{/2 ,df} = 2.6800 (From t - distribution Critical Values Table)

d)

test statistic (Z):

Z = -3.0304

P -value = 0.00122

e)

test statistic (Z) < t_critical

-3.0304 < 2.6800

and also P -value <

0.00122 < 0.01

reject the null hypothesis(H₀)

f)

test statistic (Z) < t_critical

reject the null hypothesis(H₀) , but there is not sufficient evidence to reject the claim, that beer content is 32 ounces.

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