**Hypothesis Testing for Tailored Samples**Given Hypotheses:\( H_0: \mu = 100 \)\( H_a: \mu \neq 100 \)A sample of 65 is used. Identify the p-value and state your conclusion for each of the following sample results. Use \(\alpha = 0.05\).### (a) \(\bar{x} = 104\) and \(s = 11.4\)**Find the value of the test statistic.** (Round your answer to three decimal places.)*Test Statistic:*\(\boxed{\textit{__}} \)**Find the p-value.** (Round your answer to four decimal places.)*p-value:*\(\boxed{\textit{__}} \)**State your conclusion.**- \( \circ \) Do not reject \(H_0\). There is sufficient evidence to conclude that \(\mu \neq 100\).- \( \circ \) Do not reject \(H_0\). There is insufficient evidence to conclude that \(\mu \neq 100\).- \( \circ \) Reject \(H_0\). There is sufficient evidence to conclude that \(\mu \neq 100\).- \( \circ \) Reject \(H_0\). There is insufficient evidence to conclude that \(\mu \neq 100\).### (b) \(\bar{x} = 96.5\) and \(s = 11.0\)**Find the value of the test statistic.** (Round your answer to three decimal places.)*Test Statistic:*\(\boxed{\textit{__}} \)**Find the p-value.** (Round your answer to four decimal places.)*p-value:*\(\boxed{\textit{__}} \)**State your conclusion.**- \( \circ \) Do not reject \(H_0\). There is sufficient evidence to conclude that \(\mu \neq 100\).- \( \circ \) Do not reject \(H_0\). There is insufficient evidence to conclude that \(\mu \neq 100\).- \( \circ \) Reject \(H_0\). There is sufficient evidence to conclude that \(\mu \neq 100\).- \( \circ \) Reject \(H_0\). There is insufficient evidence to conclude that \(\

a) Given data : sample size, n =65 sample mean, x̄ = 104 sample standard…

Ho: μ = 100 H₂: H 100 A sample of 65 is used. Identify the p-value and state your conclusion for each of the following sample results. Use (a) x = 104 and s = 11.4 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. O Do not reject Ho. There is sufficient evidence to conclude that μ = 100. O Do not reject Ho. There is insufficient evidence to conclude that μ # 100. H O Reject Ho. There is sufficient evidence to conclude that μ = 100. O Reject Ho. There is insufficient evidence to conclude that μ = 100. (b) x = 96.5 and s = 11.0 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. O Do not reject Ho. There is sufficient evidence to conclude that μ ‡ 100. O Do not reject Ho. There is insufficient evidence to conclude that μ = 100. O Reject Ho. There is sufficient evidence to conclude that μ ‡ 100. O Reject Ho. There is insufficient evidence to conclude that μ ‡ 100. (c) x = 102 and s = 10.4 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.)

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E