Question

# A local brewery distributes beer in bottles labeled 24 ounces. A government agency thinks that the...

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 23.6 ounces with a 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. DON'T JUST GIVE THE ANSWER - SHOW WORK AND EXPLAIN YOUR PROCESS EACH STEP OF THE WAY SO THAT I CAN FOLLOW WHAT YOU DID AND CHECK YOUR WORK.

Solution :

= 24

= 236

s = 0.70

n = 50

This is the two tailed test .

The null and alternative hypothesis is

H0 :   = 24

Ha : 24

= 0.01

The critical value for a two-tailed test is tc​=2.68.

The rejection region for this two-tailed test is = t >2.68

Test statistic = t

= ( - ) / s / n

= (23.6 - 24) /0.70 / 50

= -4.041

P (t< -4.041) = 0.0002

P-value = 0.0002

= 0.01

0.0002 < 0.01

Reject the null hypothesis .

There is sufficient evidence to suggest that the brewery is cheating its customers.