Gallup regularly conducts a poll asking American adults to rate their life on a scale of zero to ten. Zero represents the worst possible life and ten represents the best possible life. People who responded seven or above are considered "thriving". People who responded five or six are considered "struggling". People who responded four or lower are considered "suffering". The most recent poll (2018) found 4% of respondents to be suffering. The sample size was n = 1500. The sample percentage 4% is ? p x? p? Suppose that for the past three years, the percentage of respondents who were "suffering" was steady at 2.5%. State hypotheses that would lead us to test our 2018 value of 4% against the historical value of 2.5% to see whether the population percentage has increased significantly H0 : p = 4% and Ha : p < 2.5% H0 : p = 4% and Ha : p > 2.5% H0 : p = 2.5% and Ha : p < 4% H0 : p = 2.5% and Ha : p > 2.5% H0 : p = 2.5% and Ha : p < 2.5% H0 : p = 4% and Ha : p ? 4%
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59% to the current value of 4%. So, our null hypothesis (H0) would be that the population percentage has not changed, meaning it is still 2.59%. Our alternative hypothesis (Ha) would be that the population percentage has increased, meaning it is greater than Show more…
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Gallup regularly conducts a poll asking people to imagine a ladder with 10 rungs. Rung 0 represents the worst possible life and rung 10 represents the best possible life. Respondents are asked what rung they would say they are on. Responses are classified as "Thriving" (standing on rung 7 or higher, and expecting to be on rung 8 or higher five years from now), "Suffering" (standing on rung 4 or lower and expecting to be on rung 4 or lower 5 years from now), or "Struggling" (not thriving or suffering). The poll for November $22-25,2011,$ found $4 \%$ of respondents to be suffering. The polls all use a sample size of approximately 1500 people. (www.gallup .com/poll/152033/Fewer-Americans-Thriving-2011- 2010.aspx) a) Explain the meaning of $" \hat{p}=0.04$ " in the context of this situation. b) Calculate the standard error of $\hat{p}$. c) Explain what this standard error means in the context of this situation.
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