Question 259927
2.Use the method specified to perform the hypothesis test for the population 
mean . A local brewery distributes beer in bottles labeled 32 ounces. A government agency thinks that the brewery is cheating its customers. The agency select 50 of these bottles, measures their contents, and obtains a sample mean of 31.6 ounces with a population standard deviation of 0.70 ounce. At - this symbol means the level of significance alpha = 0.01, test the agency’s claim that the brewery is cheating its customers 
b. Use the P-value method. 
1. 
Ho : u=32
Ha : u < 32 (because the problem claims there is cheating which is less than 32)
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2. &#61537; = 1%
3. Test statistics:
t(31.6) =  (31.6-32)/[0.7/square root(50) = -4.0406
4. P-value or critical z0 or t0. df (-100 -4.0406.49) = 0.00009379
Note: I changed your p-value: It should be 9.378x10^-5 = 0.00009379
5. Rejection Region:
For a left tail test with alpha = 1% and df=49 the
rejection Region is t< invT(0.01,49) = -2.4049
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6. Decision: Since p < 1%, reject Ho.
7. Interpretation: 
The test results support rejecting the manufacturer's claim 
and provides strong evidence that the brewery is cheating.
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Cheers,
Stan H.