Expert answer:Stats question

Expert answer:Please help on these four stat question. Please take this seriously, I have just shut one tutor down for this assignment! I will pay enough if you can actually help. Detailed solving procedure plz!!!! Thanks!
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Stat 20 Fall 2017: Homework 5, due Friday December 1 at 8 pm.
Please turn in, a pdf file on gradescope, solutions to the following problems. Don’t forget to indicate to gradescope which page corresponds to which
problem.
1. (a) A coin is tossed 5 times, and lands heads on 4 of them. Test the
hypothesis that the coin is fair versus the alternative that it is
biased towards heads, at a significance level of 20%. Make sure
to write down the null, the alternative, the box, and the P-value.
State your conclusion carefully.
(5 points)
(b) Now, suppose the same coin is tossed 50 times, and lands heads
on 40 of those tosses. Test the same hypotheses, at the same
significance level. State your conclusion carefully.
(5 points)
(c) Now suppose the coin was actually biased, and the chance of landing heads on a toss was, in fact, 60%. What is the probability that
we would reject the null hypothesis of the coin being fair, in favor
of the coin being biased towards heads, at the significance level
defined above (20%)?
(5 points)
2. A Gallup poll conducted during December 2013 found that 51% of a
random sample of 1011 adults generally disapprove of the Affordable
Care Act (also known as Obamacare).
(a) Construct a 95% confidence interval for the true proportion of
adults in the United States who generally disapprove of Obamacare.
(3
points)
(b) What is the margin of error for this poll for the 95% confidence
level?
(1 point)
(c) If you want a 98% confidence level, will the margin of error be
smaller or larger?
(1 point)
(d) Compute that margin of error.
(2 points)
(e) In general, if all other aspects of the situation remain the same,
would smaller samples produce smaller or larger margins of error?
Explain!
(2 points)
1
3. A sample of middle-school aged boys and girls (grades 5-8) were surveyed in Ontario, Canada. Of the 1,147 boys surveyed, 688 watched
between 1 and 3 hours of television per day. Of the 1,256 girls surveyed, 796 watched between 1 and 3 hours of television per day. Is
this difference due to chance, or is there a real difference between the
genders as far as television viewing habits are concerned?
(a) Set up the box models for the two samples, clearly indicating the
sample size and count.
(2 points)
(b) What is the standard error for the percentage of boys in the sample
that watch between 1 and 3 hours of TV?
(2 points)
(c) What is the standard error for the percentage of girls in the sample
that watch between 1 and 3 hours of TV?
(2 points)
(d) Set up a test of significance, and clearly indicate the null hypothesis, the sample statistic, the observed significance level, and your
conclusion.
(4 points)
4. On the Gallup web page, the President’s approval rating is tracked.
Presidents’ popular support often increases in response to major international events, called “rally events”. President Obama apparently
had a rally since Osama Bin Laden’s death…or did he? His approval
rating before the news of Bin Laden’s death was 46%. In a poll conducted over the three days immediately following Bin Laden’s death,
Gallup conducted a survey of a random sample of 1,558 adults, and
52% of those surveyed said that they approve of the President. Is this
difference due to chance? Construct a significance test to answer this
question. Please clearly indicate the null and the alternative hypotheses, the chance model you are using, the P-value, and your conclusion
in the context of the problem. You may assume that the sample
is a simple random sample.
(5 points)
2
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