Question

A linguistics researcher would like to know if there is a difference in the proportions of Canadians and Europeans who are bilingual. In a survey of 175 randomly selected Canadians, they found that 29 are bilingual. In a survey of 125 randomly selected Europeans, they found that 27 are bilingual.

a) Define Population 1 and Population 2.

b) Define the parameter of interest.

c) Name the distribution required to calculate confidence intervals. (Check the relevant criteria.)

d) Construct a 99% confidence interval for the difference in the population proportions.

e) Interpret your confidence interval.

f) At a 99% confidence level, is there a difference in the proportions?

Answer 1

a) Population 1 refers to the population of Canadians while Population 2 refers to the population of Europeans. b) The parameter of interest is the difference in the proportions of Canadians and Europeans who are bilingual. c) The distribution required to calculate confidence intervals is the normal distribution.

Step-by-step explanation:

a) Population 1 refers to the population of Canadians while Population 2 refers to the population of Europeans.

b) The parameter of interest is the difference in the proportions of Canadians and Europeans who are bilingual.

c) To calculate confidence intervals, we need to consider the sampling distribution of the difference in proportions, which follows a normal distribution when certain conditions are met.

d) To construct a 99% confidence interval for the difference in population proportions, use the formula:

CI = (p1 - p2) ± Z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))

e) The confidence interval gives you a range of plausible values for the difference in proportions. In this case, it tells you with 99% confidence that the difference in proportions of Canadians and Europeans who are bilingual falls within the calculated interval.

f) To determine if there is a difference in proportions at a 99% confidence level, check if the confidence interval includes zero. If it does not include zero, then there is evidence of a significant difference.