You are the new owner of a restaurant. You read that a sample survey by the National Restaurant Association shows that 40% of adults are committed to eating nutritious food when eating away from home. To help plan your menu, you decide to conduct a sample survey in your own area. You will use random digit dialing to contact an SRS of 200 households by telephone.

a) If the national result holds in your area, is it reasonable to use a normal approximation for the sampling distribution? Be sure to justify your response.

Question

You are the new owner of a restaurant. You read that a sample survey by the National Restaurant Association shows that 40% of adults are committed to eating nutritious food when eating away from home. To help plan your menu, you decide to conduct a sample survey in your own area. You will use random digit dialing to contact an SRS of 200 households by telephone.

a) If the national result holds in your area, is it reasonable to use a normal approximation for the sampling distribution? Be sure to justify your response.

mathmale · Answer

Let's summarize what we know:  The population proportion is 0.40.  The sample size is 200.  There are certain criteria for deciding whether or not it is reasonable to use a normal approximation for the same distribution.   What are those criteria?   does this  situation satisfy those criteria?

mathmale · Answer

If we were discussing population and samples means, the criteria for assuming that the sample is normally distributed is n>30.  But that's a different situation from the given one.

anonymous · Answer

Yes this situation satisfies those conditions.