ECO220Y1 Final: ECO220Y1Y UTSG Final Exam220 APR18 Solution
ECO220Y1Y, APRIL 2018, FINAL EXAM: SOLUTIONS
(1) (a) We need to make an inference about the difference in population proportions. To obtain the sample proportion
for no taglines:
=.∗.∗
= 0.5386. To obtain the sample proportion for superfluous taglines:
=
.∗.∗
=0.4410. Hence, the point estimate of the difference is -0.0976, which says that people shown
misleading advertising (superfluous taglines) are nearly 10 percentage points less likely to choose the best credit card
compared to people who make the choice without being confronted with misleading advertising (no taglines).
To test for a difference (either way) requires a two-tailed test:
: −=0
: −≠0
=
(
)
(
)
where
=
=
=(∗.∗.)(∗.∗.)
=..
=.
= 0.4900
=
(
)
(
)
=..
.(.)
.(.)
=.
.
.
=.
. = −3.91
The difference is highly statistically significant at any conventional significance level (noting that the Standard Normal
table stops at z values of 3.69 as the tail areas become so tiny), including an of 0.001.
(b) We need to make an inference about the difference in population proportions. The point estimate of the difference
is 0.14, which says that among people who saw misleading advertising (superfluous taglines) those that saw the
implemental video were 14 percentage points more likely to choose the best credit card compared to people who saw
the baseline video.
(
−
)±/
(
)
+
(
)
(0.51−0.37)±2.576.(.)
+.(.)
(0.14)±2.576∗0.03477
0.14±0.0896 which gives a LCL of 0.05 and an UCL of 0.23
For people who have to make a credit card choice while faced with misleading ads, we are 99% confident that showing
them the longer (implemental) video increases the percent selecting the best credit card by between 5 and 23
percentage points compared to the shorter (baseline) video. (A causal interpretation is correct because these are
experimental data where the key x variable – which video a person watched – is randomly assigned.) While it is clear
that the longer video helps people not be distracted by misleading advertising, the width of the interval is wide: it may
increase the percent making the best choice by only 5 p.p. but it could have a huge impact of 23 p.p.
(2) This requires an inference about the difference between means for paired data: : =0 versus : ≠0 where
the correct test statistic is given by =
√
⁄.
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Eco220y1y, april 2018, final exam: solutions (1) (a) we need to make an inference about the difference in population proportions. To obtain the sample proportion for superfluous taglines: (cid:1842)(cid:3552)(cid:3047)(cid:3028)(cid:3034)= To test for a difference (either way) requires a two-tailed test: for no taglines: (cid:1842)(cid:3552)(cid:3041)(cid:3042)(cid:3047)(cid:3028)(cid:3034)=(cid:2868). (cid:2872)(cid:2871) (cid:2872)(cid:2868)(cid:2875)(cid:2878)(cid:2868). (cid:2874)(cid:2873) (cid:2871)(cid:2877)(cid:2875) (cid:2876)(cid:2868)(cid:2872) (cid:2868). (cid:2871)(cid:2875) (cid:2871)(cid:2877)(cid:2872)(cid:2878)(cid:2868). (cid:2873)(cid:2869) (cid:2872)(cid:2868)(cid:2873) (cid:2875)(cid:2877)(cid:2877) (cid:1834)(cid:2868):(cid:3435)(cid:1868)(cid:3041)(cid:3042)(cid:3047)(cid:3028)(cid:3034) (cid:1868)(cid:3047)(cid:3028)(cid:3034)(cid:3439)=0 (cid:1834)(cid:2868):(cid:3435)(cid:1868)(cid:3041)(cid:3042)(cid:3047)(cid:3028)(cid:3034) (cid:1868)(cid:3047)(cid:3028)(cid:3034)(cid:3439) 0 (cid:3495)(cid:3265)(cid:3365)((cid:3117)(cid:3127)(cid:3265)(cid:3365))(cid:3289)(cid:3117) (cid:2878)(cid:3265)(cid:3365)((cid:3117)(cid:3127)(cid:3265)(cid:3365))(cid:3289)(cid:3118) where (cid:1842)(cid:3364)=(cid:3025)(cid:3117)(cid:2878)(cid:3025)(cid:3118) (cid:1878)= (cid:3017)(cid:3552)(cid:3118)(cid:2879)(cid:3017)(cid:3552)(cid:3117) (cid:3041)(cid:3117)(cid:2878)(cid:3041)(cid:3118) (cid:1842)(cid:3364)=(cid:3025)(cid:3117)(cid:2878)(cid:3025)(cid:3118) (cid:2876)(cid:2868)(cid:2872)(cid:2878)(cid:2875)(cid:2877)(cid:2877) =(cid:2875)(cid:2876)(cid:2873). (cid:2871)(cid:2877) (cid:3041)(cid:3117)(cid:2878)(cid:3041)(cid:3118)=((cid:2872)(cid:2868)(cid:2875) (cid:2868). (cid:2872)(cid:2871)(cid:2878)(cid:2871)(cid:2877)(cid:2875) (cid:2868). (cid:2874)(cid:2873))(cid:2878)((cid:2871)(cid:2877)(cid:2872) (cid:2868). (cid:2871)(cid:2875)(cid:2878)(cid:2872)(cid:2868)(cid:2873) (cid:2868). (cid:2873)(cid:2869)) =(cid:2872)(cid:2871)(cid:2871). (cid:2868)(cid:2874)(cid:2878)(cid:2871)(cid:2873)(cid:2870). (cid:2871)(cid:2871) (cid:2869)(cid:2874)(cid:2868)(cid:2871) =0. 4900 (cid:2876)(cid:2868)(cid:2872)(cid:2878)(cid:2875)(cid:2877)(cid:2877) (cid:1878)= (cid:3495)(cid:3265)(cid:3365)((cid:3117)(cid:3127)(cid:3265)(cid:3365))(cid:3289)(cid:3117) (cid:2878)(cid:3265)(cid:3365)((cid:3117)(cid:3127)(cid:3265)(cid:3365))(cid:3289)(cid:3118) = (cid:3123)(cid:3125)(cid:3125) =(cid:2879)(cid:2868). (cid:2868)(cid:2877)(cid:2875)(cid:2874) The difference is highly statistically significant at any conventional significance level (noting that the standard normal ((cid:1842)(cid:3552)(cid:2870) (cid:1842)(cid:3552)(cid:2869)) (cid:1878)(cid:3080)/(cid:2870)(cid:3495)(cid:3017)(cid:3552)(cid:3118)((cid:2869)(cid:2879)(cid:3017)(cid:3552)(cid:3118)) (cid:3041)(cid:3118) +(cid:3017)(cid:3552)(cid:3117)((cid:2869)(cid:2879)(cid:3017)(cid:3552)(cid:3117)) (cid:3041)(cid:3117) (0. 51 0. 37) 2. 576(cid:3495)(cid:2868). (cid:2873)(cid:2869)((cid:2869)(cid:2879)(cid:2868). (cid:2873)(cid:2869)) (cid:2872)(cid:2868)(cid:2873) (0. 14) 2. 576 0. 03477. 0. 14 0. 0896 which gives a lcl of 0. 05 and an ucl of 0. 23. In panel b, the shape of the distribution from sh to is positively (right) skewed. In panel b, the shape of the distribution from . 01 to ,000 is bimodal.
