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 0.37 grain. Does this information provide strong evidence for concluding that the company is not filling its bottles as advertised? Test the appropriate hypotheses using a = 0.01 by first computing the P-value and then comparing it to the specified significance level. State the appropriate hypotheses.
a. Η₀: μ ≠ 5
Hₐ: μ = 5
b. Η₀: μ = 5
Hₐ: μ > 5
c. Η₀: μ = 5
Hₐ: μ < 5
d. Η₀: μ = 5
Hₐ: μ ≠ 5