Question

An average of 12 ounces of beer is used to fill each bottle in a local brewery as recorded. The manager now believes that, in general, beer bottles are overfilled. He takes a random sample of 30 bottles to test. The sample mean weight of the bottles is 12.8 ounces with a standard deviation of 1.5 ounces. Conduct a one-sample t-test to test whether the beer bottles are overfilled. Use 5% level of significance. (Round your steps to 4 decimal places

Answer 1

Solution:

Given n=30, X=12.8 , s=1.5

Test Hypothesis

H0 :   = 12

Ha : > 12(right tailed)

degrees of freedom = n - 1 = 30 - 1 = 29

Test statistic :

t = ( - ) / s / n

= (12.8 - 12) / 1.5 / 30

Test statistic = t = 2.921

P(t > 2.921) = 1-P (t < 2.921) = 1 - 0.9967

P-value = 0.0033

= 0.05  

P-value <

Reject the null hypothesis .

There is sufficient evidence to support the claim