Question

Complete the problems below. Show some of your steps and explain the answer, too.

Question #1 (6 points)

A 95% confidence interval for a population proportion yielded the interval (.345, .455).

1. Compute the margin of error.
2. Compute the sample proportion.
3. Will a 90% confidence interval be wider or narrower? Explain.

Question #2 (6 points)

According to recent figures, 6% of college graduates (aged 21-24) are unemployed, which is the lowest rate since before the recession. Suppose we take a random sample of 230 recent graduates (aged 21-24). What is the probability that the unemployment rate is 9% or higher? (This 9% number is significant because it was the unemployment rate for college grads during the recession.) Does it seem like the unemployment rate has improved significantly since the recession? Explain.

Question #3 (8 points)

A Pew Research Center poll of 1007 randomly selected adults showed that 42% of those survey feel the Internet is a bad influence on morality.

1. What is the value of n?
2. What is the value of p^?
3. Compute the margin of error, E, that corresponds to a 95% confidence level.
4. Compute the 95% confidence interval estimate of the population proportion p.
5. Based on the results, can we safely conclude that more than half of adults feel the Internet is a bad influence on morality?
6. Assuming you are a newspaper reporter, write a brief statement that accurately describes the results and includes all of the relevant information

Answer 1

1)a) Margin of error = (0.455 - 0.345)/2 = 0.055

b) + 0.055 = 0.455

Or, = 0.4

c) The 90% confidence interval will be narrower. Because as the confidence level decreases, the margin of error also decreases. So that the confidence interval becomes narrower.

2) p = 0.06

n = 230

= p = 0.06

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

= sqrt(0.06(1 - 0.06)/230)

= 0.0157

P( > 0.09)

= P(( - )/ > (0.09 - )/)

= P(Z > (0.09 - 0.06)/0.0157)

= P(Z > 1.91)

= 1 - P(Z < 1.91)

= 1 - 0.9719

= 0.0281

Yes, the unemployment rate has improved significantly since the recession, because the probability value is less than 0.05.

3)a) n = 1007

b) = 0.42

c) Margin of error = z0.025 * sqrt((1 - )/n)

= 1.96 * sqrt(0.42(1 - 0.42)/1007)

= 0.0305

d) The 95% confidence interval is

+/- E

= 0.42 +/- 0.0305

= 0.3895, 0.4505

e) Since the interval doesn't contain 0.5, so we Can conclude that more than half of adults feel the internet is a bad influence on morality.