Answer to Question #175767 in Statistics and Probability for Denisse Bisuña

Question

1.Describe the sampling distribution of proportions.

2.What do you understand by the expression "p is an unbiased estimator of p"?

3.What is meant by the phrase "95% confidence interval for the population p"?

4.A consumer watch group interviewed a random sample of 1,000 consumers and asked them if they are optimistic about the economy or not. There were 612 who said yes. Use 95% confidence level to estimate the population proportions.

Answer 1

1.The sampling distribution of a given population is the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population. It describes a range of possible outcomes that of a statistic, such as the mean or mode of some variable, as it truly exists a population.

2. If p has the minimum variance among all the unbiased estimators of p, so It can be said that p is an unbaise estimator of p.

3.A 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population.

4.$n=1000, p=\dfrac{612}{1000}=0.612, q=1-p=1-0.612=0.388$

$\alpha=0.05\\ Z_{\frac{\alpha}{2}}=Z_{0.025}=1.96$

Confidence interval = $p\pm Z_{0.025}\sqrt{\dfrac{pq}{n}}$

= $0.612\pm 1.96\times \sqrt{\dfrac{0.612\times 0.388}{1000}}$

$=0.612\pm 0.0302=(0.58179,0.64220)$