Question

A little confused on this hw question thank you :)

In 2017, 49% of New Jersey residents were married. A study of 1000 randomly selected NJ residents was conducted. Prove the sampling distribution for the proportion of married NJ residents is approximately normal. Show your work.

Answer 1

The sampling distribution is said to be approximately normal, if the following condition is met

n * p0 * (1 - p0) > 10

n = 1000, p0 = 49% = 0.49, and 1 - p0 = 0.51

Therefore 1000 * 0.49 * 0.51 = 249.9 which is > 10 and hence the condition for normality (or approximate) is met.

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The other requirements for doing a hypothesis test, that we need to check

(a) That the sample size is less than 5% of the population. i.e we should be able to assume that the total population of New Jersey residents who were married is more than 20,000.

(b) The sample is randomly sampled (which is mentioned)

(c) They should be independent, which is mostly assumed until otherwise mentioned

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