Question

2. After the 2016 presidential election, Gallup collected a random sample of 1,021 Americans and estimated that 47% of Americans wanted to keep the electoral college. One month before the election, in October 2016, another random poll of 1,100 Americans estimated that 52% wanted to keep the Electoral College. Statistically speaking, we can look at whether or not we can be sure that there was a change in opinions about keeping the Electoral College between October of 2016 and November of 2016. [15 points] (a) What is the point estimate for the November poll? (b) What is the point estimate for the October poll? (c) Are these point estimates statistics or parameters? Explain why or why not. (d) Report and interpret the difference between the two point estimates. (e) Compute the estimated standard error for the difference between two estimates. Show your work. (f) Construct and interpret the difference between these groups at the 95% level. Show your work. 1 Now we can also perform a significance test. (g) State the null hypothesis. (h) State an alternative hypothesis. (i) The test statistic z=-2.3012 and its associated p-value is approximately 0.021 for a two-tailed test at the 5% significance level. Interpret this result in regards to the hypotheses you stated above.

Answer 1

1- october

2- november

a)

p2^ = 0.47

b)

p1^ = 0.52

c)

statistics, this is because they are based on sample

d)

p1^ - p2^ = 0.52 - 0.47 = 0.05

e)

Standard error = 0.0217

f)

CI is (0.0075,0.0925)

g)

Ho : p1 = p2

h) Ha : p1 <> p2

i)

since p-value = 0.021 < alpha

we reject the null hypothesis

we conclude that there is significant difference

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