Question

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 $np0$and $n(1-p0)$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

The required correct option is $\left(d\right)$

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

Step-by-step solution

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 $b$explains the large counts rule, whereas option $d$explains the central limit theorem. Only options $b$and $d$are 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 $d$does not satisfy the significance test condition for the given specific set of data.

Conclusion

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

The correct option is $\left(d\right)$