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 sample size and the Central Limit Theorem.
The Central Limit Theorem states that when the sample size is sufficiently large (typically greater than or equal to 30), the sampling distribution of a population proportion (p) is approximately normal, regardless of the shape of the population distribution.
In this case, the statement claims that a sample size of 900 is not large enough to conclude that the sampling distribution of p is normal when the estimate of the population proportion is 0.995. To verify this, we can apply the guidelines of the Central Limit Theorem.
To estimate if a sample size is large enough, we need to examine the expected number of successes and failures in the sample. The general rule of thumb suggests that both the number of successes (n * p) and failures (n * (1 - p)) should be greater than or equal to 10, where 'n' is the sample size and 'p' is the estimated population proportion.
In this case, the estimated population proportion is 0.995, and the sample size is 900. Multiplying these values, we get approximately 896.55, which satisfies the guideline of having more than 10 successes. Similarly, the number of failures can be calculated by subtracting the number of successes from the sample size (900 - 896.55), resulting in 3.45, which is less than 10.
Based on the guideline, the sample size of 900 is indeed large enough to conclude that the sampling distribution of p is approximately normal, given the estimate of the population proportion of 0.995. Therefore, the statement is false, as the sample size is adequate for the Central Limit Theorem to apply.