Exercise 3 A test for the variance can be done based on thefollowing rejection rules: Case (a) Case (b) Case (c) H0 : σ 2 ≤ σ2 0 (or σ 2 = σ 2 0 ) H0 : σ 2 ≥ σ 2 0 (or σ 2 = σ 2 0 ) H0 : σ 2 =σ 2 0 H1 : σ 2 > σ2 0 H1 : σ 2 < σ2 0 H1 : σ 2 6= σ 2 0Reject if (n − 1)S 2 σ 2 0 > χ2 n−1,α (n − 1)S 2 σ 2 0 < χ2n−1,1−α (n − 1)S 2 σ 2 0 < χ2 n−1,1−α/2 or (n − 1)S 2 σ 2 0 >χ2 n−1,α/2 Use this test to solve the following problem: Apharmaceutical company is concerned about the variability of thecontent of the active ingredient in a new allergy medication theyplan to submit for approval to the FDA. Even though certain levelof variability is not a problem, if there is evidence that thestandard deviation of the content exceeds 0.1mg, the FDA would notapprove the new medication. The pharmaceutical company’s managerswant to make sure that the new medication will get the approvalbefore submitting it because, otherwise, the reputation of thecompany would be seriously damaged and, therefore, conduct a testat the 1% significance level to try to prove that, at this level ofsignificance, they can prove that the variability is below thestandards required by the FDA. (a) Propose a null and analternative hypothesis to test the safety of the medication (notethat the test is written for the variance and not for the standarddeviation!). (b) The company takes a sample of 100 pills andmeasures the content of the active ingredient in all of them,obtaining a standard deviation of 0.085mg. Is this enough evidenceat the 1% significance level to say that the variability is belowthe FDA requirements? (c) Find and interpret the p-value of thistest. Should the company submit the medication?