Questions: Does a population have to be normally distributed in order to use the chi-square distribution? Choose the correct answer below. A. No, the population can have any distribution to use the chi-square distribution. B. Yes, in order to use the chi-square distribution, the population must be normally distributed. C. No, in order to use the chi-square distribution, the population must have a standard normal distribution. D. No, in order to use the chi-square distribution, the population must be exponentially distributed.

Does a population have to be normally distributed in order to use the chi-square distribution? Choose the correct answer below. A. No, the population can have any distribution to use the chi-square distribution. B. Yes, in order to use the chi-square distribution, the population must be normally distributed. C. No, in order to use the chi-square distribution, the population must have a standard normal distribution. D. No, in order to use the chi-square distribution, the population must be exponentially distributed.
Transcript text: Does a population have to be normally distributed in order to use the chi-square distribution? Choose the correct answer below. A. No, the population can have any distribution to use the chi-square distribution. B. Yes, in order to use the chi-square distribution, the population must be normally distributed. C. No, in order to use the chi-square distribution, the population must have a standard normal distribution. D. No, in order to use the chi-square distribution, the population must be exponentially distributed.
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Solution

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Solution Steps

Step 1: Understand the Nature of the Chi-Square Distribution

The chi-square distribution is primarily used in hypothesis testing and in constructing confidence intervals for certain types of problems, particularly those involving categorical data and variance estimates in normally distributed populations.

Step 2: Identify the Specific Context

The specific context in which the chi-square distribution is being applied is categorical data analysis.

Step 3: Review the Assumptions

For the goodness-of-fit test, The data should be in the form of frequencies or counts of categories.

Step 4: Requirements for Using the Chi-Square Distribution

For most chi-square test applications, The requirement is not on the population being normally distributed but rather on the expected frequencies or the sample size being sufficiently large.

Final Answer:

To use the chi-square distribution for goodness-of-fit, it is essential to The requirement is not on the population being normally distributed but rather on the expected frequencies or the sample size being sufficiently large.. This is based on the assumption that The data should be in the form of frequencies or counts of categories.

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