A brewery claims that the consumers are getting a mean volume equal to 32 ounces of beer in their quart bottles. The Bureau of Weights and Measures randomly selects 36 bottles and obtains the following measures in ounces: 32.09 31.89 31.06 32.03 31.42 31.39 31.75 31.53 32.42 31.56 31.95 32.00 31.39 32.09 31.67 31.47 32.45 32.14 31.86 32.09 32.34 32.00 30.95 33.53 32.17 31.81 31.78 32.64 31.06 32.64 32.20 32.11 31.42 32.09 33.00 32.06 Test the claim of the brewery about the mean volume equal to 32 oz. at the 0.05 significance level. a. Null Hypothesis; b. Alternate Hypothesis: c. Complete Picture- draw the normal curve, label the critical value and test statistic. d. Test statistic: e. Statistical Conclusion: f. Explanation of Conclusion: 2. A medical researcher claims that fewer than 20% of adults taking a certain medication will experience side effects. In a random sample of 400 adults who use this particular medication, 68 adults experienced the side effects. Test the researcher Solution A) I would use T-test because dispersion is unknown. alfa = 0.05 (significance level) n = 36 Xavg = 31.95 (evaluation of mean volume) S = 0.53 (evaluation of dispersion) H0 ... a0 = 32 (First hypothesis is that expected mean volume is the one that brewery claims, 32) H1 ... a < a0 (Second hypothesis is that expected mean volume is lower than volume that brewery claims. This is hypothesis we are testing.) T = (Xavg - a0) * (sqrt(n)) / S = -0.61 There are 3 conditions for discarding hypothesis H0: 1. H1 ... a <> a0 : | t\' | > t\'_[n-1 , 1 - alfa/2] 2. H1 ... a < a0 : t\' < -t\'_[n-1 , 1- alfa] (our case) 3. H1 ... a > a0 : t\' > t\'_[n-1 , 1- alfa] --------------------------------------.

1. A brewery claims that the consumers are getting a mean volume equal to 32 ounces
of beer in their quart bottles. The Bureau of Weights and Measures randomly selects 36 bottles
and obtains the following measures in ounces:
32.09 31.89 31.06 32.03 31.42 31.39 31.75
31.53 32.42 31.56 31.95 32.00 31.39 32.09
31.67 31.47 32.45 32.14 31.86 32.09 32.34
32.00 30.95 33.53 32.17 31.81 31.78 32.64
31.06 32.64 32.20 32.11 31.42 32.09 33.00
32.06
Test the claim of the brewery about the mean volume equal to 32 oz. at the 0.05 significance
level.
a. Null Hypothesis;
b. Alternate Hypothesis:
c. Complete Picture- draw the normal curve, label the critical value and test statistic.
d. Test statistic:
e. Statistical Conclusion:
f. Explanation of Conclusion:

2. 2. A medical researcher claims that fewer than 20% of adults taking a certain
medication will experience side effects. In a random sample of 400 adults who use this
particular medication, 68 adults experienced the side effects. Test the researcher
Solution
A)
I would use T-test because dispersion is unknown.
alfa = 0.05 (significance level)
n = 36
Xavg = 31.95 (evaluation of mean volume)
S = 0.53 (evaluation of dispersion)
H0 ... a0 = 32 (First hypothesis is that expected mean volume is the one that brewery claims, 32)
H1 ... a < a0 (Second hypothesis is that expected mean volume is lower than volume that
brewery claims. This is hypothesis we are testing.)
T = (Xavg - a0) * (sqrt(n)) / S = -0.61
There are 3 conditions for discarding hypothesis H0:
1. H1 ... a <> a0 : | t' | > t'_[n-1 , 1 - alfa/2]
2. H1 ... a < a0 : t' < -t'_[n-1 , 1- alfa] (our case)
3. H1 ... a > a0 : t' > t'_[n-1 , 1- alfa]
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