Question

A researcher believes that 9%

of females smoke cigarettes.

If the researcher is correct, what is the probability that the proportion of smokers in a sample of 703
females would differ from the population proportion by more than 3%?

Answer 1

To find the probability that the proportion of smokers in a sample of 703 females would differ from the population proportion by more than 3%, calculate the standard error of the proportion and use the z-score formula.

Step-by-step explanation:

To find the probability that the proportion of smokers in a sample of 703 females would differ from the population proportion by more than 3%, we can use the normal approximation to the binomial distribution. First, calculate the standard error of the proportion:

Standard Error = sqrt(p_hat * (1-p_hat) / n)

Where p_hat is the estimated proportion (0.09), and n is the sample size (703).

Then, find the z-score corresponding to a difference of 3%:

Z = (p_sample - p_population) / SE

Where p_sample is the sample proportion, p_population is the population proportion, and SE is the standard error.

Finally, find the probability using the standard normal distribution table or calculator.