Question

8a. Means - A brewery distributes beer in bottles labeled 10 ounces. Some people think they are getting less than they pay for. The local Bureau of Weights and Measures randomly selects 70 of these bottles, measures their contents and obtains a sample mean of 9.9 ounces. Assuming that σ is known to be 0.10 ounces, is it valid at a 0.05 significance level to conclude that the brewery is cheating the consumer?

8b. (Means) A bottling company distributes pop in bottles labeled 10 ounces. The company thinks people are getting than they paid for. The company randomly selects 35 of these bottles, measures their contents and obtains a sample mean of 10.1 ounces and a sample standard deviation of 0.20 ounces, is it valid at a 0.05 significance level to conclude that the company is giving the customer more than what they paid for?

Answer 1

10 10 t9.9 8a) Null hypothesis;HO Alternative hypothesis H1: Sample mean Population s.d Sample size: Level of significance: Critical value Decision rule: Reject HO if Test statistic: μ- μ< 70 0.05 1.645 1.645 α- Z< 1-837 Decision: reject HO Conclusion It is valid

8b)Null hypothesis;Ho: Alternative hypothesis,H1 sample mean Sample size: Sample s.d: Degrees of freedom Level of significancee μ> 10 x 10.1 n- 35 S0.2 n-134 00.05 a1.691 Decision rule Reject HO if t1.691 Critical value: Test statistic: x-μ - 2.958 71 Decision: Reject HO Conclusion: Yes it is valid Note: If σ is known then we use z distribution otherwise t distribution