Gender and color preference

Gender and color preference#

A study asked 1967 male and 3809 female undergraduate college students their favorite color. A 95% confidence interval for the difference between the proportions of males and females whose favorite color is black \((p\_{male} - p\_{female})\) was calculated to be (-0.03, 0.03). Based on this information, determine if the following statements about undergraduate college students are true or false.

Part 1#

We are 95% confident that the true proportion of males whose favorite color is black is 3.0% lower to 3.0% higher than the true proportion of females whose favorite color is black.

Answer Section#

  • False

  • True

Part 2#

We are 95% confident that the true proportion of males whose favorite color is black is 3.0% to 3.0% higher than the true proportion of females whose favorite color is black.

Answer Section#

  • True

  • False

Part 3#

95% of random samples will produce 95% confidence intervals that include the true difference between the population proportions of males and females whose favorite color is black.

Answer Section#

  • True

  • False

Part 4#

We can conclude that there is a significant difference between the proportions of males and females whose favorite color is black and that the difference between the two sample proportions is too large to plausibly be due to chance.

Answer Section#

  • True

  • False

Part 5#

The 95% confidence interval for \((p\_{female} - p\_{male})\) cannot be calculated with only the information given in this exercise.

Answer Section#

  • False

  • True

Attribution#

Problem is from the OpenIntro Statistics textbook, licensed under the CC-BY 4.0 license.
Image representing the Creative Commons 4.0 BY license.