Question

A town council wants to estimate the proportion of residents who are in favor of a proposal to upgrade the computers in the town library. A random sample of 100 residents was selected, and 97 of those selected indicated that they were in favor of the proposal. Is it appropriate to assume that the sampling distribution of the sample proportion is approximately normal?A. No, because the sample is not large enough to satisfy the normality conditions.

B. No, because the size of the population is not known.
C. Yes, because the sample was selected at random.
D. Yes, because sampling distributions of proportions are modeled with a normal model.
E. Yes, because the sample is large enough to satisfy the normality conditions.

Answer 1

Answer: E. Yes, because the sample is large enough to satisfy the normality conditions

Explanation:

The Central Limit Theorem states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger. The requirement is usually pegged at when number of samples is greater than or equal to 30. From the information given, sample size = 100

Therefore, it appropriate to assume that the sampling distribution of the sample proportion is approximately normal

E) because the sample is large enough to satisfy the normality conditions