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Chapter 11: Problem 10

Explain the difference between the observed and expected frequencies for a goodness-of-fit test.

Short Answer

Expert verified
In a goodness-of-fit test, observed frequencies are the actual data counts obtained from a sample, while expected frequencies are the theoretically calculated counts we would expect if the null hypothesis is true. The difference between them is used to determine whether the observed data fits the theoretical expectation.

Step by step solution

01

Definition of Observed Frequencies

Observed frequencies refer to the actual count in each category obtained from a sample data. This is actual data collected in the form of responses, behaviors, observations, etc. or the numbers we've counted in a study or experiment.
02

Definition of Expected Frequencies

Expected frequencies are the theoretical frequencies or counts that we would expect to obtain if the null hypothesis of a goodness-of-fit test is true. They are usually calculated or derived based on some theoretical expectation, assumption or model, rather than direct measurement or observation.
03

Difference between Observed and Expected Frequencies

The main difference between observed and expected frequencies lies in the source of its generation. Observed frequencies are derived directly from the data, they are what we see or measure. Expected frequencies, on the other hand, are not directly observable but calculated based on a theoretical assumption or null hypothesis. The difference between these two frequencies is used in a goodness-of-fit test to determine whether our observed data fits a particular theoretical expectation or not.

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Most popular questions from this chapter

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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A sample of seven passengers boarding a domestic flight produced the following data on weights (in pounds) of their carry-on bags. \(\begin{array}{lllllll}46.3 & 41.5 & 39.7 & 31.0 & 40.6 & 35.8 & 43.2\end{array}\) a. Using the formula from Chapter 3, find the sample variance, \(s^{2}\), for these data. b. Make the \(98 \%\) confidence intervals for the population variance and standard deviation. Assume that the population from which this sample is selected is normally distributed. c. Test at a \(5 \%\) significance level whether the population variance is larger than 20 square pounds.
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