Math Problem Statement

Consider the following hypotheses and the sample data in the accompanying table. Answer the following questions using alpha ​= 0.02. LOADING... Click the icon to view the data table. Upper H 0​: mu equals 10 Upper H 1​: mu not equals 10 ​a) Determine the critical​ value(s). The critical​ value(s) is(are)    enter your response here. ​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

Solution

To solve this problem, let's work step-by-step:

Hypotheses:

  • H0:μ=10H_0: \mu = 10 (null hypothesis)
  • H1:μ10H_1: \mu \neq 10 (alternative hypothesis)

This is a two-tailed test since the alternative hypothesis specifies μ10\mu \neq 10.

Significance Level:

The significance level is α=0.02\alpha = 0.02.

Critical Value Determination:

  1. Critical Region:

    • For a two-tailed test, the total significance level α\alpha is split equally between the two tails: α/2=0.01\alpha/2 = 0.01 in each tail.
  2. **Determine the ( z

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Two-Tailed Test
Critical Values

Formulas

Z = (X̄ - μ) / (σ / √n)
Critical Z-values for a two-tailed test

Theorems

Standard Normal Distribution
Critical Value Theorem

Suitable Grade Level

Undergraduate (Introductory Statistics)