Question

6. A recent Gallop poll showed Trump's approval rating 40% with a margin or error of 3%. a) Find the confidence interval. c) Does the confidence interval support that more than 50% of Americans approve of Trump? Why or why not? 7. A recent Gallop poll showed that 672 of 1019 adults nationwide think that marijuana should be legalized. a) Find the margin of error that corresponds to a 95% confidence interval. c) Find the 95% confidence interval estimate of the proportion of adults nationwide who think marijuana should be legalized.

Answer 1

Question 6

Part a)

Proportion P = 40% = 0.4

Margin of error = 3% = 0.03

Confidence interval = ( 0.4 - 0.03 , 0.4 + 0.03 )

Confidence interval is ( 0.37 , 0.43 )

Part c)

Since the values of confidence interval is less than 0.5, hence there is insufficient evidence to support that more than 50% of Americans approve of Trump.

Question 7

Part a)

Margin of Error = Z(α/2) √ ( (p*q) / n) = 0.0291
Z(α/2) = Z(0.05/2) = 1.96

Part c)

p̂ = X / n = 672/1019 = 0.6595
p̂ ± Z(α/2) √( (p * q) / n)
0.6595 ± Z(0.05/2) √( (0.6595 * 0.3405) / 1019)
Z(α/2) = Z(0.05/2) = 1.96
Lower Limit = 0.6595 - Z(0.05) √( (0.6595 * 0.3405) / 1019) = 0.6304
upper Limit = 0.6595 + Z(0.05) √( (0.6595 * 0.3405) / 1019) = 0.6886
95% Confidence interval is ( 0.6304 , 0.6886 )
( 0.6304 < P < 0.6886 )