Question

please solve both questions 4&5 and solve all parts.

4) Your company manufactures 200 mg ibuprofen tablets. You randomly sample 25 tablets and measure their mass, then calculate the average mass X from this sample. You know that the standard deviation of tablet mass from your manufacturing process is ơ- 0 mg a. Specify a null and alternative process to determine whether or the mass of ibuprofen tablets from your process is 200 mg b. You reject the null hypothesis Ho: 200 mg if the average mass of 25 tablets X falls outside the range of 200 ± 2 mg. What is the type I error probability α? Find the value ofAx so that the type I error probability null hypothesis Ho: μ-200 mg if the average mass of 25 tablets X falls outside the range of 200 Ακ mg c. -0.05 or 5% if you reject the d. You hope your test is powerful enough to detect a 5 mg change in the mean tablet mass μ, so you specify the alternative to be Hi: μ-195 or μ-205 mg. What is the type II error probability B if you decide to reject the null hypothesis if the average mass of 25 tablets X falls outside the range of 200 2 mg? What change in mass can be detected if type II error probability B - 0.05? In other words, find ΔΧ so that an alternative of Hi : μ-200-Δχ or μ-200 + Δχ will result in a type II error probability β-0.05 if you reject the null hypothesis when the average mass of 25 tablets X falls outside the range of 200 ± 2 mg e. 5) Provide answers for the following scenarios. You do not have to do any calculations; only provide estimates or guesses that would be consistent with the information provided. You must explain vour answers to receive full credit: You are testing Ho: μ-5 vs. Hi: μ < 5. The critical value of the sample mean is X-4 for a test level α-0.05, and your sampling results in a value of X that leads you to reject the null hypothesis. Provide estimates for the statistic X, an estimate for the 95% confidence interval for u and the p-value that would satisfy this scenario. a. b. You are testing Ho: p-0.6 vs. Hi: p test level of α 0.01 because you obtained a statistic value X-325 out of 500 samples. Provide an estimate for the critical value(s) of the statistic X that satisfies this scenario 0.6. You failed to reject the null hypothesis for a You are testing Ho: σ standard deviation S-1.8 which results in a p-value of 0.035 for this test. State whether or not you are rejecting the null hypothesis Ho: σ-12, and provide estimates for the critical value(s) of the sample standard deviation S and the 95% confidence interval that satisfy this scenario c. 1.2 vs. Hi : σ > 1.2, test-level of α-0.05, and obtain a sample d. You are testing Ho: p alternative hypothesis Hi, the level of the test a, whether or not you are rejecting the null hypothesis Ho: p 0.45, provide estimates for the critical value(s) of the sample proportion p that satisfy this scenario. 0.45 and obtain a 99% confidence interval p < 0.48. State the

Answer 1

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reket Ho Eto O 95 2- 2 2 스X' 0.95 2 16 (200-2 r 2to42) 18 C 又 c 202 118 XC202 P a8-115 202-17s 2- 25

に145 (ex-9117674) ← (2x ,7331928) s 11 412