**PLEASE show all work/steps and fully explain** An aspirin manufacturer fills b
ID: 3387483 • Letter: #
Question
**PLEASE show all work/steps and fully explain** An aspirin manufacturer fills bottles by weight rather than by count. Since each bottle should contain 100 tablets, the average weight per tablet should be 5 grains. Each of 100 tablets taken from a very large lot is weighed, resulting in a sample average weight per tablet of 4.87 grains and a sample standard deviation of .35 grain. Does this information provide strong evidence for concluding that the company is not filling its bottles as advertised? Test the appropriate hypotheses using alpha = .01 by first computing the P-value and then comparing it to the specified significance level.Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u = 5
Ha: u =/ 5
As we can see, this is a two tailed test.
Thus, getting the critical z, as alpha = 0.01 ,
alpha/2 = 0.005
zcrit = +/- 2.575829304
Getting the test statistic, as
X = sample mean = 4.87
uo = hypothesized mean = 5
n = sample size = 100
s = standard deviation = 0.35
Thus, z = (X - uo) * sqrt(n) / s = -3.714285714
Also, the p value is
p = 0.000203778
As |z| > 2.576, and P < 0.01, we REJECT THE NULL HYPOTHESIS.
Thus, there is significant evidnece that the company is not filling its bottles as advertised, the mean is not 5 grains at 0.01 level. [CONCLUSION]
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