Statistics - Chapter 7 - Section 7.5

In a random sample of 39 Democrats from one city, 30 approved of the mayor's performance. In a random sample of 50 Republicans from the city, 32 approved of the mayor's performance. Find a 90% confidence interval for the difference between the proportions of Democrats and Republicans who approve of the mayor's performance.

• (0.609, 0.929)

• (0.579, 0.957)

• (-0.028, 0.287)

• (0.582, 0.957)

A survey found that 27 of 71 randomly selected women and 48 of 72 randomly selected men follow a regular exercise program. Find a 95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program.

• (-0.443, -0.130)

• (0.194, 0.567)

• (-0.473, 0.567)

• (0.223, 0.537)

A polling agency wants to compare support for the president's foreign policies between men and women. They surveyed 2500 U.S. citizens and found a 95% confidence interval for the difference in proportions between men and women who support the president's foreign policies as (-0.05 to -0.025) where population 1 is men and population 2 is women. Select the correct interpretation of this result.

• The interval does not contain 0, which shows that there is no significant difference in the proportions between men and women.

• 2. The number surveyed should be increased to increase the accuracy of the confidence interval.

• 2. The interval estimates that p₁ – p₂ < 0 which shows that women are more likely than men to support with

     the president's foreign policies.

• 2. The interval estimates that p₁ – p₂ < 0 which shows that men are more likely than women to support with

     the president's foreign policies.

94. A polling agency wants to estimate the proportion of U.S. citizens who support the president's domestic policies. They surveyed 2500 U.S. citizens and found a 95% confidence interval for the difference in proportions between men and women who support the president's domestic policies as (-0.025 to 0.050) where population 1 is men and population 2 is women. Select the correct interpretation of this result.

• 0. The interval does not contain zero which shows that there is no significant difference in the proportions between men and women.

• 2. The interval contains zero which shows that men are more likely than women to disagree with the president's foreign policies.

• 2. The interval contains zero which shows that women are more likely than men to disagree with the president's foreign policies.

• 2. The interval contains zero which shows that there is no significant difference in the proportions between men and women.

94. A medical study examined data on patients with cardiovascular disease who were currently non-smokers and those who were current smokers. Population 1 were smokers and population 2 were non-smokers. After data analysis, the 95% confidence interval for the difference in proportions is 0.015 +/- 0.011. The most accurate interpretation is...

• 0. We are 95% confident that the difference in the proportion of smokers compared to nonsmokers is between 0.004 and 0.026. There is a significance difference indicating higher cardiovascular disease amongst smokers.

• 0. We are 95% confident that the interval of the difference in the proportions contains zero. There is not a significance difference between smokers and non-smokers.

• 0. We are 95% confident that the proportion of smokers compared to non-smokers is between 0.004 and 0.026.

• 0. We are 95% confident that the difference in the proportion of smokers compared to nonsmokers is between

     -0.004 and 0.026. There is not a significance difference in the proportions.