Question

3. Let X.X, ^ Erp^). A company claims that the lifetime of their lightbulbs is longer than the lifetime of the leading brand, which is six years. You are going to test the hypothesis: Ho S 6,Ha : μ > 6. (a) Assume n > 30. We know from the CLT that X ~ N(μ, σ2/n). Show that nX ~ N(n,1,nơ2). (b) You are going to perforin a hypothesis test using Σ.ī instead of X. What is your test statistic and decision rule for determining whether the hypothesis should be rejected? (c) Perform the test of hypothesis with α 0.005 using your test procedure, with n = 45 5%, 312.85, and s-7.45. (d) What is the p-value of your test? Provide an interpretation of this p-value

Answer 1

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