Final answer:
The assertion p(n) could be part of a mathematical proposition, but more context is needed. In hypothesis testing of a single population proportion, the conditions np > 5 and nq > 5 must be met for normal approximation. The p-value indicates the probability of observing results, given the null hypothesis is true.
Step-by-step explanation:
Define p(n) to be an assertion refers to making a statement or proposition about a particular mathematical property that is true for all natural numbers n.
However, without additional context, the specificity of the assertion p(n) cannot be determined. In the realm of hypothesis testing, particularly when testing a single population proportion, certain conditions must be met for the distribution of the sample proportion p' to be approximated by a normal distribution.
These conditions include a sufficiently large sample size such that the products np and nq (where q = 1 - p and p is the population proportion) are both greater than five.
This ensures that the sampling distribution of the sample proportion can be approximated using a normal distribution. Here, x represents the number of successes in the sample, and n represents the sample size, making the sample proportion p' = x/n.
The hypothesis test involves the null hypothesis (H0) that assumes no effect or no difference, and an alternative hypothesis (Ha) that states what you suspect might be true instead.
The p-value is a crucial concept in this area of statistics, representing the probability of obtaining results at least as extreme as the observed ones, under the assumption that the null hypothesis is true. A lower p-value indicates stronger evidence against the null hypothesis.
When evaluating a hypothesis test, it's beneficial to consider the p-value, among other factors, to determine if the null hypothesis can be rejected.