Is there a rule to figure out if this is a true or false statement?

A sample size of 900 is not large enough to conclude that the sampling distribution of p is a normal distribution, when the estimate of the population proportion is .995.

To determine if the statement is true or false, we need to understand the concept of the sampling distribution and the conditions required for it to be approximately normal.

The sampling distribution refers to the distribution of a sample statistic, such as the sample proportion (p), when repeated samples are taken from the same population. In this case, we estimate the population proportion to be 0.995.

To assess whether the sampling distribution of p is approximately normal, we typically consider two main conditions:

1. Random Sampling: The samples must be selected randomly from the population. This ensures that the sample is representative of the population and helps to avoid bias.

2. Sample Size: The sample size should be sufficiently large. Specifically, we need to check if the product of the sample size (n) and the estimated population proportion (p-hat = 0.995) meets certain criteria.

In general, if both np-hat and n(1-p-hat) are greater than or equal to 10, then the sampling distribution of the sample proportion can usually be assumed to be approximately normal.

Now let's calculate the values using the given information:

n = sample size = 900
p-hat = estimate of the population proportion = 0.995

np-hat = 900 * 0.995 = 895.5
n(1-p-hat) = 900 * (1-0.995) = 4.5

Based on these calculations, we find that both np-hat and n(1-p-hat) are greater than or equal to 10. Therefore, we can conclude that the sample size of 900 is indeed large enough to assume that the sampling distribution of p is approximately normal.

Hence, the given statement is false.