A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 50 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 52.2 milligrams. Assume the population is normally distributed and the population standard deviation is 7.9 milligrams. At α = 0.09, can you reject the company's claim? Complete parts (a) through (e).(a) Identify \( H_0 \) and \( H_a \). Choose the correct answer below.- F. \( H_0: \mu = 50 \)- \( H_a: \mu \neq 50 \)(b) Find the critical value(s). Select the correct choice below and fill in the answer box within your choice.(Round to two decimal places as needed.)- A. The critical values are \( \pm \) [box].[Correct choice highlighted as F and "box" left for student input.]

Name: A company that makes cola drinks states that the mean caffeine conten
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Description: A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 50 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine

Introduction: Denote μ as the true population mean caffeine content in 12-ounce bottles of cola. The null and alternative hypotheses based on the given claim, as correctly selected by you, are: H0: μ = 50; vs, Ha: μ ≠ 50.Calculation: The sample size, that is, the number of 12-ounce bottles is, n = 30. The sample mean caffeine content is X̅ = 52.2 milligrams. The population standard deviation is σ = 7.9 milligrams. The significance level is α = 0.09. The observed standardized test statistic for this test is: z observed = (x̅ – μ)/ (σ/√n) = (52.2 – 50) / (7.9/√30) = (2.2) / (7.9/√30) ≈ 1.53. Thus, the standardized test statistic is, 1.53. For significance level α, the critical values for the two-tailed z-test are –zα/2 and zα/2, such that, P (| Z | ≥ zα/2) = α, with P (Z ≥ zα/2) = α/2, that is, P (Z < zα/2) = 1 – α/2, and P (Z ≤ –zα/2) = α/2. Here, since is α = 0.09, is α/2 = 0.045. This implies that, P (Z ≥ z0.045) = 0.045, that is, P (Z < z0.045) = 0.955 (= 1 – 0.045). Also, P (Z ≤ –z0.045) = 0.045. Using the standard normal distribution table or the Excel formula: =NORM.S.INV(0.045), it can be found that –z0.045 ≈ –1.70. As a result, z0.045 = 1.70. Thus, the critical value are ± 1.70. Decision rule using critical values: Reject H0 at significance level α, if z ≤ –z0.045 or z ≥ z0.045. Otherwise, fail to reject H0. Since observed z (≈ 1.53) < z0.045 (≈ 1.70), fail to reject H0. Thus, there is not enough evidence to reject the company’s claim that the mean caffeine content in 12-ounce bottles is 50 milligrams, at 0.09 significance level.

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A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 50 milligrams. You want to test this claim. During your tests, you find that population standard deviation is 7.9 milligrams. At a = 0.09, can you reject the company's claim? Complete parts (a) through (e). random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 52.2 milligrams. Assume the population is normally distributed and the (a) Identify Ho and Ha. Choose the correct answer below. O A. Ho: H*52.2 HaiH = 52.2 O B. Ho: H# 50 HaiH = 50 0. H : με 52.2 Ha: H#52.2 Ο D. Ho μ 52.2 Ha:H< 52.2 O E. Ho: H2 50 HaiH< 50 F. Ho: H= 50 Ha:H# 50 (b) Find the critical value(s). Select the correct choice below and fill in the answer box within your choice. (Round to two decimal places as needed.) O A. The critical values are t O B. The critical value is

A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 50 milligrams. You want to test this claim. During your tests, you find that population standard deviation is 7.9 milligrams. At a = 0.09, can you reject the company's claim? Complete parts (a) through (e). random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 52.2 milligrams. Assume the population is normally distributed and the (a) Identify Ho and Ha. Choose the correct answer below. O A. Ho: H*52.2 HaiH = 52.2 O B. Ho: H# 50 HaiH = 50 0. H : με 52.2 Ha: H#52.2 Ο D. Ho μ 52.2 Ha:H< 52.2 O E. Ho: H2 50 HaiH< 50 F. Ho: H= 50 Ha:H# 50 (b) Find the critical value(s). Select the correct choice below and fill in the answer box within your choice. (Round to two decimal places as needed.) O A. The critical values are t O B. The critical value is

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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