**Testing a Claim about the Population Mean**We are testing the claim about the population mean, μ, at a given level of significance using the provided sample statistics.**Claim:** μ = 30; **Level of significance (α):** 0.07; **Population standard deviation (σ):** 3.02; **Sample statistics:** Sample mean (\( \bar{x} \)): 29.7; Sample size (n): 65 **Identify the Null and Alternative Hypotheses** Choose the correct answer below:- A. \( H_0 \): μ < 30 \( H_a \): μ = 30 - B. \( H_0 \): μ = 30 \( H_a \): μ < 30 - C. \( H_0 \): μ ≠ 30 \( H_a \): μ = 30 - D. \( H_0 \): μ = 30 \( H_a \): μ ≠ 30 ✔️- E. \( H_0 \): μ > 30 \( H_a \): μ = 30 - F. \( H_0 \): μ = 30 \( H_a \): μ > 30 **Calculate the Standardized Test Statistic** The standardized test statistic is [ ].*(Round to two decimal places as needed.)*

Denote μ as the population mean.Null hypothesis: H0: μ = 30 (claim). Alternative hypothesis: Ha: μ ≠ 30. Correct option is D. Here, the population standard deviation is known. Hence, to estimate the population mean one can use z test. The sample size is n = 65. The population standard deviation is σ = 3.02. The sample size is, n = 65 and the sample mean is, x̅ = 29.7. The z-test statistic is: z = (x̅ – μ)/ (σ/√n) = (29.7 – 30)/(3.02/√65) = –0.3/0.374585 ≈ –0.80. The test statistic is –0.80. Consider that the level of significance is 0.07. Using the Excel formula, =2*(NORM.S.DIST(-0.80,TRUE)), the p-value is 0.4237. If the p-value is less than or equal to the level of significance, then reject the null hypothesis. Otherwise, failed to reject the null hypothesis. As the p-value of 0.4237 is greater than the level of significance of 0.07, then fail to reject the null hypothesis. There is not sufficient evidence against the claim that the population mean is equal to 30, at 7% level of significance.

Math

Statistics

Test the claim about the population mean, µ, at the given level of significance using the given sample statistics Claim: = 30; a = 0.07; o= 3.02. Sample statistics: x= 29.7, n= 65 Identify the null and alternative hypotheses. Choose the correct answer below. A. Ho:µ<30 Hai µ= 30 В. Но: 330 Haiµ< 30 O C. Ho: µ#30 Ha: u= 30 'D. H: μ 30 Ha: u# 30 E. H0: μ> 30 HaiH= 30 F. Ho: µ= 30 Hai µ> 30 Calculate the standardized test statistic. The standardized test statistic is . (Round to two decimal places as needed.)

Test the claim about the population mean, µ, at the given level of significance using the given sample statistics Claim: = 30; a = 0.07; o= 3.02. Sample statistics: x= 29.7, n= 65 Identify the null and alternative hypotheses. Choose the correct answer below. A. Ho:µ<30 Hai µ= 30 В. Но: 330 Haiµ< 30 O C. Ho: µ#30 Ha: u= 30 'D. H: μ 30 Ha: u# 30 E. H0: μ> 30 HaiH= 30 F. Ho: µ= 30 Hai µ> 30 Calculate the standardized test statistic. The standardized test statistic is . (Round to two decimal places as needed.)

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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