Hypothesis Test for Standard Deviation: Left-Tailed Test with Sample Size 12

Math Problem Statement

A random sample of size 12 from a normal distribution has a standard deviation s = 52. Test H0: σ = 69 versus H1: σ < 69. Use the α = 0.05 level of significance.

Solution

The problem in the image involves conducting a hypothesis test for a population standard deviation based on a random sample of size 12, where the null hypothesis $H_0: \sigma = 69$ is being tested against the alternative hypothesis $H_1: \sigma < 69$ , making it a left-tailed test. The significance level is $\alpha = 0.05$ , and the sample standard deviation is given as $s = 52$ .

This

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Standard Deviation
Left-Tailed Test

Formulas

Chi-Square Test for Standard Deviation: χ² = (n - 1) * s² / σ²
Critical Value: Based on χ² distribution table with α = 0.05 and degrees of freedom (df) = n - 1

Theorems

Chi-Square Distribution

Suitable Grade Level

Undergraduate Level - Statistics

Related Recommendation

Left-Tailed Hypothesis Test for Population Standard Deviation: Example with Chi-Square Test

Chi-square Test for Variance: Hypothesis Testing with Sample Standard Deviation

Chi-Square Test for Variance with Hypotheses σ² = 100

Chi-Square Test for Variance with Sample Standard Deviation 50.6 and Population Standard Deviation 53

Chi-Square Test for Variance: Hypothesis Testing Example with Step-by-Step Solution