Answer to Question #175348 in Statistics and Probability for Denisse Bisuña

Question

1. Which of these illustrates confidence interval?

a. 0.95

b. 99%

c. 50.0

d. 90 - 95

2.What is the effect of the level of confidence on the confidence interval?

3.What is the margin of error E?

4.Given the information that a sampled population is normally distributed with X = 36, σ = 3 and n = 20.

a. What is the 95% confidence interval for μ?

b. Are the assumptions met? Explain

Answer 1

1. b. 99%

2. Increasing the confidence will increase the margin of error resulting in a wider interval. Increasing the confidence will decrease the margin of error resulting in a narrower interval.

3. The margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The larger the margin of error, the less confidence one should have that a poll result would reflect the result of a survey of the entire population.

4. n = 20

$\bar{X} = 36$

σ = 3

In this case, the level of confidence can be defined as,

1 - α = 0.95

α = 0.05

The value of the confidence coefficient with 95% level of confidence is computed by using the standard normal z table,

$z_{α/2} = z_{0.05/2} \\ = z_{0.025} \\ = 1.96$

a. The 95% confidence interval for the mean is

$36 - (1.96)\frac{3}{\sqrt{20}} < μ < 36 + (1.96) \frac{3}{\sqrt{20}} \\ 36 - 1.31 < μ < 36 + 1.31 \\ 34.69 < μ < 37.31$

b. There are 2 requirements to use the x-proportion interval: random sample and large enough sample.