**Question 1**

Pennsylvania is a key battleground state for the upcoming presidential election. As of October 16, RCP reports the state polls have the proportion of supporters for Biden at 51% and Trump at 46%. Assume a sample size of 3000 for this poll. Z=1.96 Please label your answers.

Construct a 95% confidence interval for the Population Proportion of support for Biden. Lower limit Upper limit

Construct a 95% confidence interval for the Population Proportion of support for Trump. Lower limit Upper limit

Can we say there is more support for either candidate in Pennsylvania? Explain.

Question 2

answer part 2 frq styed please and show work

1. Because of the constantly evolving political climate around the United States, Gallup *(who regularly conducts polls in the U.S.)* conducted a poll just after the inauguration asking U.S. adults if they approve of the initiatives President Biden had implemented in his first few days in office. Another Gallup poll was conducted now that President Biden has been in office for a month asking U.S. adults if they approve of the initiatives President Biden had implemented after his first month in office. According to the first Gallup poll of 1500 randomly selected U.S. adults, 64% approved of the initiatives President Biden had implemented in his first few days in office. And according to the second Gallop poll of 1700 U.S. adults, 54% approved of the initiatives President Biden had implemented after his first month in office.

Construct and interpret a 95% confidence interval for the change (difference) in the true proportion of U.S. adults who approved of the initiatives President Biden had implemented in his first few days in office to after his first month in office.

Based on your interval, what conclusion would you make about whether President Biden’s approval rating has changed. Justify your answer.

Question 3

A laptop manufacturer claims that the mean life of the battery for a certain model of laptop is more than 5 hours. What is the claim as a mathematical statement

Answer to question 1

Answer to question 2

3) no, we cannot say there is more support for either candidate in Pennsylvania because none of intervals has both ends more than 0.50

Answer to question 3

Step 1 Claim: the mean life of the battery for a certain model of laptop is more than 5 hours.

Step 2 Claim: μ>5