The U.S. federal ban on assault weapons expired in September 2004, which meant that after 10...

The U.S. federal ban on assault weapons expired in September 2004, which meant that after 10 years (since the ban was instituted in 1994) there were certain types of guns that could be manufactured legally again. A poll asked a random sample of 1,200 eligible voters (among other questions) whether they were satisfied with the fact that the law had expired. The datafile linked below contains the results of this poll (Data were generated based on a poll conducted by NBC News/Wall Street Journal Poll). We would like to estimate p, the proportion of U.S. eligible voters who were satisfied with the expiration of the law, with a 95% confidence interval.

M.E.= 2.9%

(a) How many of the 1,200 sampled voters were satisfied?

(b) What is the sample proportion (p-hat) of those who were satisfied?

(c) What is the 95% confidence interval for p? Interpret this interval.

In question 1 you found that the margin of error of this poll was about 2.9%. What is the margin of error of the confidence interval you found in question 2?

Expert Solution

a.
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.05 is = 1.96
Sample Proportion = 0.5
ME = 0.029
n = ( 1.96 / 0.029 )^2 * 0.5*0.5
= 1141.974 ~ 1142
b.
possible chances (x)=1142
sample size(n)=1200
success rate ( p )= x/n = 0.952
c.
TRADITIONAL METHOD
given that,
possible chances (x)=1142
sample size(n)=1200
success rate ( p )= x/n = 0.952
I.
sample proportion = 0.952
standard error = Sqrt ( (0.952*0.048) /1200) )
= 0.006
II.
margin of error = Z a/2 * (standard error)
where,
Za/2 = Z-table value
level of significance, α = 0.05
from standard normal table, two tailed z α/2 =1.96
margin of error = 1.96 * 0.006
= 0.012
III.
CI = [ p ± margin of error ]
confidence interval = [0.952 ± 0.012]
= [ 0.94 , 0.964]
-----------------------------------------------------------------------------------------------
DIRECT METHOD
given that,
possible chances (x)=1142
sample size(n)=1200
success rate ( p )= x/n = 0.952
CI = confidence interval
confidence interval = [ 0.952 ± 1.96 * Sqrt ( (0.952*0.048) /1200) ) ]
= [0.952 - 1.96 * Sqrt ( (0.952*0.048) /1200) , 0.952 + 1.96 * Sqrt ( (0.952*0.048) /1200) ]
= [0.94 , 0.964]
-----------------------------------------------------------------------------------------------
interpretations:
1. We are 95% sure that the interval [ 0.94 , 0.964] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population proportion
Answer:
marin of error is 0.012

orchestra answered 2 years ago

WXY Inc. declared a dividend on July 27, 2004 to be payable on September 10, 2004....

WXY Inc. declared a dividend on July 27, 2004 to be payable on September 10, 2004. The list of shareholders who would be entitled to this dividend would be prepared on August 10, 2004. a) Identify the key dates involved with dividend payment (4 points) b) If Tom bought some shares on August 7, 2004, would he have received the dividend declared for this period? If not, who would receive it? (3 points) c) You buy a share of stock...

For the fiscal year that ended on September 30, 2017 the U.S. federal deficit was $666...

For the fiscal year that ended on September 30, 2017 the U.S. federal deficit was $666 billion, an increase of $80 billion from 2016. This was the second consecutive year the deficit has increased, following several years of decline. (The deficit was over $1 trillion in 2012 and had fallen to $438 billion in 2015, but the current deficit is more than $500 billion higher than the $161 billion deficit in 2007, the year the Great Recession began.) The Congressional...

After September 11, 2001, U.S. consumers showed a desire to tone down their consumer activities. They...

After September 11, 2001, U.S. consumers showed a desire to tone down their consumer activities. They ordered simpler foods in restaurants and spent more time at home. Therefore, a lot of marketing campaigns began emphasizing down-home themes. At some point after a disaster, it is time to get back to business. But, major catastrophic events are likely to leave permanent changes on consumers and employees in those areas. Suppose you are approached by the owner of several delicatessens and full-service...

On September 10, 2009, U.S. Treasury Bonds futures for Dec 2009 delivery was traded at 116-20...

On September 10, 2009, U.S. Treasury Bonds futures for Dec 2009 delivery was traded at 116-20 at CBOT. On September 13, the futures was traded at 114-29. You opened your position by taking 10 long positions on the T-bond futures on Sept 10. As of Sept 10, the initial margin is $4,995 per contract and the maintenance margin is $3,700. i) Calculate your gains (losses) on your position as of September 13. ii) What is the highest price at which...

The day after the U.S. stock market crash of October 19, 1987, Federal Reserve Board Chairman...

The day after the U.S. stock market crash of October 19, 1987, Federal Reserve Board Chairman Alan Greenspan issued the following statement: “The Federal Reserve, consistent with its responsibilities as the nation’s central bank, affirmed today its readiness to serve as a source of liquidity to support the economic and financial system.” What school of thought may prompt that statement? That is, which school (or schools) has a role for active monetary policy?

49. Which body is responsible for formulating U.S. monetary policy? (a) the Federal Reserve Bank of...

49. Which body is responsible for formulating U.S. monetary policy? (a) the Federal Reserve Bank of New York; (b) the Federal Open Market Committee; (c) the Secretary of the Treasury; (d) the International Monetary Fund. 50. One characteristic of the U.S. central bank is its: (a) control by the White House; (b) acceptance of appropriations from the Congress; (c) independence within the government; (d) dominance by large banks on its boards of directors. 51. Which of the following is not...

Refer to the table below, which lists the U.S. federal income tax rates for the different...

Refer to the table below, which lists the U.S. federal income tax rates for the different income brackets. If the highest point on the Laffer curve corresponds to a tax rate of 30%, then which of the following statements must be false? Taxable income brackets Tax rate 1 10% 2 15% 3 25% 4 28% 5 33% 6 35% A) Increasing tax rates across all income tax brackets will cause a greater impact on tax revenue per return for the...

The Bill of Rights contains the first 10 amendments to the U.S. Constitution, which can be...

The Bill of Rights contains the first 10 amendments to the U.S. Constitution, which can be seen below: Bill of Rights The first ten amendments to the U.S. Constitution make up what is known as the Bill of Rights. These amendments form part of the essence of what makes United States citizenship the privilege that it is. Many people are familiar with freedom of speech, freedom of religion, and freedom of the press, but these important Constitutional amendments offer more...

You deposit $13,000 annually into a life insurance fund for the next 10 years, after which...

You deposit $13,000 annually into a life insurance fund for the next 10 years, after which time you plan to retire. a. If the deposits are made at the beginning of the year and earn an interest rate of 6 percent, what will be the amount in the retirement fund at the end of year 10? b. Instead of a lump sum, you wish to receive annuities for the next 20 years (years 11 through 30). What is the constant...

Mitch is a 10-year-old with leukemia, which, after considerable treatment, is now considered a terminal condition...

Mitch is a 10-year-old with leukemia, which, after considerable treatment, is now considered a terminal condition for him. In the 2 years since his diagnosis, his parents, and other family members have focused on being optimistic around him and have asked his healthcare professionals to do the same. No one has discussed with Mitch the possibility that he might not survive his leukemia. Registered Nurse Teresa is Mitch's primary nurse during his current hospitalization for an infection. Teresa has developed...

Question