Question 256632
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  = 0.01, test the agency’s claim that the brewery is cheating its customers 
a. Use the critical value z0 method from the normal distribution
1. H0 : u = 32 
Ha : u < 32
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2. &#61537; = this means standard deviation
3. Test statistics:
t(31.6) = (31.6-32)/[0.7/sqrt(50)] = -4.0406...
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4. P-value or critical z0 or t0.
p-value = P(t<-4.0406 with df = 49) = tcdf(-100,-4.0406,49)=0.00009379
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5. Rejection Region:
The left-tail cutoff for 1% in the t-distribution for df=49 is -2.40489..
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6. Decision: Since the p-value is less than 1% reject Ho.
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7. Interpretation: This test shows evidence that the brewery is
cheating its customers.
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Cheers,
Stan H.