6.25 Gender and color preference: A 2001 study asked 1,924 male and 3,666 female
ID: 3247719 • Letter: 6
Question
6.25 Gender and color preference: A 2001 study asked 1,924 male and 3,666 female under graduate college students their favorite color. A 95% confidence interval for the difference between the proportions of males and females whose favorite col or is black (Pmale - Pfemale) was calculated to be (0.02, 0.06). Based on this information, determine if the following statements are true or false, and explain your reasoning for each statement you identify as false. (Ellis, 2001) (a) We are 95% confident that the true proportion of males whose favorite color is black is 2% lower to 6% higher than the true proportion of females whose favorite color is black. Ofalse Otrue (b) We are 95% confident that the true proportion of males whose favorite color is black is 2% to 6% higher than the true proportion of females whose favorite color is black. Ofalse OtrueExplanation / Answer
The 95% confidence interval of 'pmale - pfemale' represents that if you randomly sample 1924 males, 3666 females several times and ask them their favorite color then 95% of times the true difference in the proportion of their favorite color to be black would lie in this interval. In other words, this interval has a 0.95 probability of containing the actual difference in the proportion of males having black color and females having black as their favorite color.
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a) False
Reason - The second part is wrong as the confidence interval has positive ends which means that the proportion of men having black as favorite color is significantly greater than that of females at 0.05 level of significance.
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b) True
Reason - As explained earlier, this interval has 0.95 probability of containig the actual difference of proportions. So, we can be 95% confident that the true proportion of males whose favorite color is black is 2% to 6% higher than the true proportion of females whose favorite color is black.
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c) True
This is the definition itself. The interval indicates that 95% of the times, the 95% confidence interval would have the population difference of proportion.
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d) True
Reason - Note that the interval doesn't have the value 0, which makes the difference between the proportion of males having black as favorite and females having black as fvorite significantly different.
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e) False
Reason - It would just be negative of the confidence interval of the one that we have.
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