2. Based on a poll of registered voters in a large city, 120 out of a random sample of 250 women intended to vote for Donald Trump in the 2020 presidential electionand 132 out of a random sample of 240 men intended to vote for Donald Trump.A Is there convincing evidence that there is a difference in the proportion of all women and the proportion of all men in this city who intended to vote for Trumpn inthe 2020 presidential election at the a = 0.05 level?B. Based on your conclusion, what type of error could you have just made? Describe a consequence of making this type of error.Drouious

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Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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2. Based on a poll of registered voters in a large city, 120 out of a random sample of 250 women intended to vote for Donald Trump in the 2020 presidential election
and 132 out of a random sample of 240 men intended to vote for Donald Trump.
A Is there convincing evidence that there is a difference in the proportion of all women and the proportion of all men in this city who intended to vote for Trumpn in
the 2020 presidential election at the a = 0.05 level?
B. Based on your conclusion, what type of error could you have just made? Describe a consequence of making this type of error.
Drouious

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$N u l l h y p o t h e s i s : T h e r e i s n o d i f f e r e n c e i n t h e p r o p o r t i o n w h o i n t e n d e d t o v o t e f o r T r u m p a m o n g m a l e a n d f e m a l e P_{M} = P_{F} A l t e r n a t i v e h y p o t h e s i s : T h e r e i s a d i f f e r e n c e i n t h e p r o p o r t i o n w h o i n t e n d e d t o v o t e f o r T r u m a m o n g m a l e a n d f e m a l e . P_{M} \neq P_{F} Z - t e s t f o r t w o p r o p o r t i o n i s u s e d t o t e s t t h e a b o v e h y p o t h e s i s P_{M = \frac{132}{240} = 0.55} P_{F} = \frac{120}{250} = 0.48 P o o l e d p r o p o r t i o n = P = \frac{132 + 120}{240 + 250} = 0.5143 T e s t s t a t i s t i c s : Z = \frac{0.55 - 0.48}{\sqrt{0.5143 (1 - 0.5143) ((\frac{1}{240} + \frac{1}{250}))}} = 1.5498$

P-value of Z-statistics for two tailed is 0.1212

Since the p-value is greater than 0.05 level of significance, the

result is not significant at P<.05

Hence we fails to reject the null hypothesis and conclude that there is no difference in the proportion who intended to vote for Trump among male and female P_M=P_F

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