3. Birmingham claimed that the Commonwealth Games which highlighted the region has improved the image of the city amongst residents. In a random sample of 102 residents asked before the games 68 reported that they though Birmingham was a good place to live. After the games, in an independent sample, 89 out of 115 reported that Birmingham was a good place to live. (a) At the 5% significance level, test the hypothesis of no difference in the proportion of people reporting Birmingham was a good place to live between before and after the Commonwealth Games, against a suitable 1-sided alternative that the Games had a positive effect of the perceptions of the city.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Chapter10: Statistics
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3. Birmingham claimed that the Commonwealth Games which highlighted the region has
improved the image of the city amongst residents. In a random sample of 102 residents asked
before the games 68 reported that they though Birmingham was a good place to live. After
the games, in an independent sample, 89 out of 115 reported that Birmingham was a good
place to live.
(a) At the 5% significance level, test the hypothesis of no difference in the proportion of
people reporting Birmingham was a good place to live between before and after the
Commonwealth Games, against a suitable 1-sided alternative that the Games had a
positive effect of the perceptions of the city.
Transcribed Image Text:3. Birmingham claimed that the Commonwealth Games which highlighted the region has improved the image of the city amongst residents. In a random sample of 102 residents asked before the games 68 reported that they though Birmingham was a good place to live. After the games, in an independent sample, 89 out of 115 reported that Birmingham was a good place to live. (a) At the 5% significance level, test the hypothesis of no difference in the proportion of people reporting Birmingham was a good place to live between before and after the Commonwealth Games, against a suitable 1-sided alternative that the Games had a positive effect of the perceptions of the city.
(b) Calculate the power of the test in (a) if the true proportion reporting Birmingham is a
good place to live before and after the Games was 65% and 75%, respectively.
(c) Diagrammatically represent your answer to (b), you need to label the null hypothesis,
the true mean, the significance level, the probability of a Type II error and the power.
(d) Assuming you want the same sample sizes across the two surveys and you want a power
of 80% and given the true proportion reporting Birmingham is a good place to live
before and after the Games was 65% and 75%, respectively, what sample size would be
needed?
Transcribed Image Text:(b) Calculate the power of the test in (a) if the true proportion reporting Birmingham is a good place to live before and after the Games was 65% and 75%, respectively. (c) Diagrammatically represent your answer to (b), you need to label the null hypothesis, the true mean, the significance level, the probability of a Type II error and the power. (d) Assuming you want the same sample sizes across the two surveys and you want a power of 80% and given the true proportion reporting Birmingham is a good place to live before and after the Games was 65% and 75%, respectively, what sample size would be needed?
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