The average waiting time in a doctor’s office varies. The...

Name: Problem 66, Chapter 11: Introductory Statistics
Uploaded: 2020-12-29T15:22:32-08:00
Duration: 2 min 50 s
Channel: Evelyn Cunningham
Description: The average waiting time in a doctor’s office varies. The standard deviation of waiting times in a doctor’s office is 3.4 minutes. A random sample of 30 patients in the doctor’s office has a standard deviation of waiting times of 4.1 minutes. One doctor believes the variance of waiting times is greater than originally thought. What is the test statistic?

The average waiting time in a doctor’s office varies. The standard deviation of waiting times in a doctor’s office is 3.4 minutes. A random sample of 30 patients in the doctor’s office has a standard deviation of waiting times of 4.1 minutes. One doctor believes the variance of waiting times is greater than originally thought. What is the test statistic?

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Key Concepts

Hypothesis Testing for Variance

This concept involves testing whether the variability in a population matches a hypothesized value. In such tests, sample data are used to determine if there's sufficient evidence to conclude that the population variance differs from a specified value.

Chi-square Test for Variance

The chi-square test for variance is a statistical method used to assess whether a sample variance is consistent with a hypothesized population variance. Under the assumption of normality, the test statistic follows a chi-square distribution, enabling decision-making about the variance.

Degrees of Freedom

Degrees of freedom in the context of variance testing refer to the number of independent values in the sample that are free to vary when estimating a statistical parameter. Typically, for a variance test, it is calculated as n - 1, where n is the sample size.

Test Statistic Formula

The test statistic for comparing a sample variance to a hypothesized population variance is given by the formula (n-1)*s^2/?0^2. Here, n represents the sample size, s^2 is the observed sample variance, and ?0^2 is the hypothesized population variance, forming the basis of the chi-square test.

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