Question

1a) What must be true about the sampling method and the values of p and n in order to construct a confidence interval for a proportion? [3 bullets]

1b) Why is 0.5 used in place of p when determining the minimum sample size necessary for a proportion confidence interval?

1c) Why should you be wary of surveys that do not report a margin of error? [2]

Answer 1

1a)

np > 10

n(1-p) > 10

The sampling method is simple random sampling and sample size is large

then the distribution of sample proportion will be approximately normally distributed with mean p and standard deviation of , i.e.,

b)

other way to look at this is

n = z^2* p*q/e^2

here z and e are fixed , since we don't know p/q

we make conservative approach

and take the value of p which maximizes n

pq is maximum when p=q = 0.5

hence when we don't know prior estimate, then sample size required is larger

c)

Margin of error shows the accuracy of the results provided. Less the error, more the accuracy. So survey which does not report margin of error is not reliable on the accuarcy.

Surveys are typically designed to provide an estimate of the true value of one or more characteristics of a population at a given time. The target of a survey might be

• the average value of a measurable quantity, such as annual 1998 income or SAT scores for a particular group.
• a proportion, such as the proportion of likely voters having a certain viewpoint in a mayoral election
• the percentage of children under three years of age immunized for polio in 1997

An estimate from a survey is unlikely to exactly equal the true population quantity of interest for a variety of reasons. For one thing, the questions maybe badly worded. For another, some people who are supposed to be in the sample may not be at home, or even if they are, they may refuse to participate or may not tell the truth. These are sources of "nonsampling error."

But the estimate will probably still differ from the true value, even if all nonsampling errors could be eliminated. This is because data in a survey are collected from only some-but not all-members of the population to make data collection cheaper or faster, usually both.

The "margin of error" is a common summary of sampling error, referred to regularly in the media, which quantifies uncertainty about a survey result. The margin of error can be interpreted by making use of ideas from the laws of probability or the "laws of chance," as they are sometimes called.

Surveys are often conducted by starting out with a list (known as the "sampling frame") of all units in the population and choosing a sample. In opinion polls, this list often consists of all possible phone numbers in a certain geographic area (both listed and unlisted numbers).