Topics include non-parametric statistical inference, including the chi-square probability distribution and its goodness of fit test.

In order to apply goodness of fit testing methods,how must the sample be collected?What one adverb describes the nature of the data gathering?[eight letters]

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As a second requirement, in order to apply goodness of fit testing methods,what is theminimum numberof values in each category?(If some categories have fewer than this number, they can be merged in order to continue with the testing.)Report the answer as a CountingNumber.

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A general manager of a local supermarket chain is studying the method of payment used by the customers at two of its city stores.At the chain's downtown store last week, a sample of 400 patrons was randomly selected, and each patron's method of payment was identified.Is there sufficient evidence to dispute the claim, using a 0.001 level of significance, that all methods of payment had an equal likelihood of occurrence?The multinomial sample results were as follows:

Payment Method Cash Check Credit Card Debit Card Food Stamps

Observed Frequency 119 107 71 55 48

Given that all five methods of payment are claimed to have the same likelihood of occurrence, their respective hypothesized proportions areor20%or0.20.Therefore, what is the expected value for each category?

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What are the degrees of freedom (df) for this context?

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What is the total value of the test statistic?Express the answer without rounding, since the answer is a terminating decimal.As a courtesy,here is the expanded distribution with observed and expected values.

Payment Method Cash Check Credit Card Debit Card Food Stamps

Observed Frequency 119 107 71 55 48

Expected Frequency 80 80 80 80 80

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Report the corresponding critical value for the indicated level of significance, rounding to the nearest hundredth.

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Report thep-value rounded to the nearest thousandth, expressed as a decimal.:#.###

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What is the most appropriate technical conclusionfor this hypothesis test,based on the available evidence and testing at the indicated level of significance?

1. Highly fail to reject the null hypothesis.
2. Fail to reject the null hypothesis.
3. Marginally fail to reject the null hypothesis.
4. Marginally reject the null hypothesis.
5. Reject the null hypiothesis.
6. Highly reject the null hypothesis.
7. No conclusion can be drawn based on the evidence.

What is the most appropriate contextual conclusionfor this hypothesis test,based on the available evidence and testing at the indicated level of significance?

It is highly unreasonable that the payment methods are equallylikely.

It isunreasonable that the payment methods areequallylikely.

It is marginallyunreasonable that the payment methods areequallylikely.

It is marginallyreasonable that the payment methods areequallylikely.

It isreasonable that the payment methods areequallylikely.

It is highlyreasonable that the payment methods areequallylikely.

No conclusion can be drawn based on the evidence.