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# Gallup found in 2013 that 58% of Americans worry a great deal or a fair amount about global warming, up from 55% in 2012. Results for this Gallup poll were based on telephone interviews performed on March $7-10,2013$, with a random sample of 1022 adults, aged 18 and older, living in the United States. Does the increase from 2012 to 2013 show a substantial increase in concern?e) Do you think this difference is meaningful? Explain.

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In this item, we are given a scenario where a study in 2013 found that the proportion of Americans worrying with a great deal or fair amount about global warming is $0.58$. This proportion is then up from the previous proportion of $0.55$ in 2012. The study was then conducted with a sample of $1022$ adults chosen randomly.

As such, we denote the following values.

• $p_0=0.55$
• $\hat p=0.58$
• $n=1022$

For this item, we are then tasked to conduct a one-proportion $z$-test to determine whether the increase in proportion from 2012 to 2013 is significant.

From the previous parts, we obtained a $z$ test statistic of $1.93$ and a $p-value$ of $0.0268$. As such, we concluded that the increase in the proportion of concerned American adults from 2012 to 2013 is significant.

For this part, we are tasked to give our thoughts regarding whether the increase between the 2012 proportion $(0.55)$ and 2013 proportion $(0.58)$ is meaningful or not.

When do we say that the difference between proportions is meaningful?

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