Chapter 10, Problem T10.3SPT

To determine

To select the correct option for, which of the following is not a condition for performing the significance test.

Answer to Problem T10.3SPT

Option (a) is correct.

Explanation of Solution

The conditions for performing a two sample z test are: Random, Normal and Independent.

Thus, we can say by looking at the question that,

Random: It is satisfied because according to the given question the samples have been to be random samples.

Normal: It is also satisfied because according to the given question the number of successes $\left(35,15\right)$ and failures $\left(183-35=148,136-15=121\right)$ are at least $10$ .

Independent: It is satisfied because the sample sizes are less than $10\%$ of the population size.

Thus all expect the option (a) has been satisfied. But (a) option cannot be satisfied because the number of successes is not close to half the sample size and thus the distribution is not symmetrical nor normal. Thus the correct option is (a) option.