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Chapter 11: Problem 9

What is a goodness-of-fit test and when is it applied? Explain.

Short Answer

Expert verified
A goodness-of-fit test is a statistical method used to verify if observed sample data coincides with the expected distribution based on a certain hypothesis. It's applied when there's a need to ascertain if a data set aligns with theoretical predictions, fits a specific distribution, or to check if certain categories occur at the desired frequencies.

Step by step solution

01

Defining a Goodness-of-Fit Test

At the core, a goodness-of-fit test is a statistical approach used to compare observed data with the expected outcome based on a specific theoretical model. Fundamentally, it is a method to test whether the observed sample data are consistent with an hypothesized distribution.
02

Explaining the Use Cases

Goodness-of-fit tests are most often applied when there's a need to decide if a random sample matches the expected distribution. Examples include testing whether data fits a normal distribution, verifying if experimental results match the expected outcomes, or to assess if particular categories occur with specific frequencies.
03

Elaborating on the Importance

Understanding the goodness-of-fit test becomes pivotal in statistical analysis because it provides a foundation to decision making based on observed data. When the goodness-of-fit test indicates that a data set significantly adheres to a specific distribution, further statistical procedures appropriate for that distribution can be employed.

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Most popular questions from this chapter

Determine the value of \(\chi^{2}\) for 23 degrees of freedom and an area of \(.990\) in the left tail of the chisquare distribution curve.

An auto manufacturing company wants to estimate the variance of miles per gallon for its auto model AST727. A random sample of 22 cars of this model showed that the variance of miles per gallon for these cars is .62. Assume that the miles per gallon for all such cars are (approximately) normally distributed. a. Construct the \(95 \%\) confidence intervals for the population variance and standard deviation. b. Test at a \(1 \%\) significance level whether the sample result indicates that the population variance is different from \(.30\).

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Two drugs were administered to two groups of randomly assigned 60 and 40 patients, respectively, to cure the same disease. The following table gives information about the number of patients who were cured and not cured by each of the two drugs. $$ \begin{array}{lcc} \hline & \text { Cured } & \text { Not Cured } \\ \hline \text { Drug I } & 44 & 16 \\ \text { Drug II } & 18 & 22 \\ \hline \end{array} $$
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