Question

186 of 310 New York state residents who were randomly sampled believe the state should legalize marijuana. Create a 98% confidence interval for the true proportion of NY state residents who believe in legalizing marijuana.

List the requirements necessary to create the confidence interval.
a) Random sampling from the population.
b) Normality assumption of the sampling distribution.
c) Sufficiently large sample size.

Answer 1

To create a 98% confidence interval for the true proportion of NY state residents who believe in legalizing marijuana, the requirements are random sampling from the population, normality assumption of the sampling distribution, and sufficiently large sample size.

Step-by-step explanation:

To create a 98% confidence interval for the true proportion of NY state residents who believe in legalizing marijuana, there are three requirements:

1. Random sampling from the population: The sample of 310 New York state residents should have been randomly chosen to avoid bias.
2. Normality assumption of the sampling distribution: The sampling distribution of the proportion should be approximately normal, which can be satisfied if the sample size is large enough (see next requirement).
3. Sufficiently large sample size: In this case, the sample size is 310, which is larger than the suggested minimum sample size of 30 needed for the normality assumption to hold.