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Chapter 9: Q. 60. (page 584)

Which of choices (a) through (d) is not a condition for performing a significance test about a population proportion p?

a. The data should come from a random sample from the population of interest.

b. Both np0and n(1-p0)should be at least 10.

c. If you are sampling without replacement from a finite population, then you should sample less than 10%of the population.

d. The population distribution should be approximately Normal unless the sample size is large.

e. All of the above are conditions for performing a significance test about a population proportion.

Short Answer

Expert verified

The required correct option is (d)

The population distribution should be approximately Normal unless the sample size is large.

Step by step solution

01

The objective is to find out the correct option which does not show a condition for performing a population proportion's significance test.

The question concerns the population proportion. You must check whether the given sample is a random sample or not using the population proportion.

Option bexplains the large counts rule, whereas option dexplains the central limit theorem. Only options band dare satisfied when the data is normal.

Only large counts can be used with probabilities. The Central Limit theorem is applied to data with a sampling distribution of means.

However, the problem condition is one of population proportion or probability. As a result, option B states the correct condition for performing a significance test. And option ddoes not satisfy the significance test condition for the given specific set of data.

02

Conclusion

Unless the sample size is large, the population distribution should be roughly Normal.

The correct option is (d)

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