6. Is there a difference in the average age that people get married in the United States and its close neighbor, Canada? Suppose a random sample of 30 Americans had an average age of marriage of 28 years with standard deviation 3 years. For a random sample of 30 Canadians, the average age was 30.1 years with standard deviation 3.3 years. (a) Construct a $$ 95 \% $$ confidence interval for the difference in average age of marriage between Canadians and Americans. (b) Interpret the interval. (c) Based on the interval, do you expect there to be evidence or little to no evidence for $$ H_{a} $$ : $$ \mu_{1}
eq \mu_{2} $$ ? Explain without conducting the hypothesis test.

Question

6. Is there a difference in the average age that people get married in the United States and its close neighbor, Canada? Suppose a random sample of 30 Americans had an average age of marriage of 28 years with standard deviation 3 years. For a random sample of 30 Canadians, the average age was 30.1 years with standard deviation 3.3 years. (a) Construct a $$ 95 \% $$ confidence interval for the difference in average age of marriage between Canadians and Americans. (b) Interpret the interval. (c) Based on the interval, do you expect there to be evidence or little to no evidence for $$ H_{a} $$ : $$ \mu_{1} 
eq \mu_{2} $$ ? Explain without conducting the hypothesis test.

Lee Mejia · Accepted Answer

The 95% confidence interval for the difference in average age of marriage between Canadians and Americans is approximately $$ (0.454, 3.746) $$. This interval does not include zero, suggesting a statistically significant difference in the average ages of marriage, with Canadians marrying later than Americans.

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