Question

researchers plan to estimate the proportion of people in a large community who don't wear a seatbelt while driving although it is unknown by the researcher, the true proportion is p=.20

a) suppose the researchers plan to estimate p from a random sample of n=200 drivers. find the mean and standard deviation of the sampling distribution of the sample proportion.

b) use the empirical rule to fill in the blanks in the following sentence: in about 95% of all random samples of size n=200 from this population, the sample proportion of people who dont use a seatbelt is between _____and_____

Answer 1

a) p = 0.20

n = 200

= p = 0.20

= sqrt(p(1 - p)/n)

= sqrt(0.2(1 - 0.2)/200)

= 0.0283

b) According to the empirical rule about 95% of the data fall within 2 standard deviation from the mean.

= 0.2 - 2 * 0.0283 = 0.1434

= 0.2 + 2 * 0.0283 = 0.2566

95% of all random samples of size n = 200 from this population the sample proportion of people who don't use a seatbelt is between 0.1434 and 0.2566.