Chapter 9.2, Problem 60E

To determine

The correct option which does not show a condition for performing a population proportion’s significance test is:

1. The data should come from a random sample or randomized experiment.
2. Both $n{p}_0$ and $n\left(1-p_0\right)$ should be at least $10$ .
3. If you are sampling without replacement from a finite population, then you should sample no more than of the $10\%$ population.
4. The population distribution should be approximately Normal, unless the sample size is large.
5. All of the above are conditions for performing a significance test about a population proportion.

Answer to Problem 60E

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

Explanation of Solution

The question is asked about the population proportion. You have to verify that the given sample is either random sample or not with the population proportion.

Option b gives the large counts rule whereas the option d tells that central limit theorem. When the data is normal only then two options b and d satisfied.

With the probabilities the large counts can only be used. Data with the sampling distribution of means is used for the Central Limit theorem.

But the problem condition is regarding to population proportion or probability. So the option B states correct condition for the performing a significance test. And the option d not satisfies the condition of the significance test about the given specific set of data.

Conclusion:

Hence, the correct option is d.