Question

A study1 of transgender adults examines the age at which they began to transition and the age of their earliest memories of gender dysphoria. (In this exercise, we examine the age beginning transition and in Exercise 6.107 we examine the age of their earliest memories.) In the study of 210 transgender adults, the mean age at which they began transitioning was 32.6 with a standard deviation of 18.2. Find a 95% confidence interval for the mean age at which transgender adults begin transitioning.

1 Zaliznyak M, Bresee C, and Garcia MM, "Age at First Experienceof Gender Dysphoria Among Transgender Adults Seeking Gender-Affirming Surgery," JAMA Network Open, March 16,2020. Some of the data has been approximated from informationin the paper.

Answer 1

The 95% confidence interval for the mean age at which transgender adults begin transitioning is approximately (30.131, 35.069).

To find the 95% confidence interval for the mean age at which transgender adults begin transitioning, we can use the formula:

Confidence Interval = mean ± (critical value) * (standard deviation / sqrt(sample size))

Given that the mean age of transitioning is 32.6, the standard deviation is 18.2, and the sample size is 210, we need to find the critical value to use in the formula.

Since we are looking for a 95% confidence interval, we can find the critical value using a standard normal distribution table or a calculator.

The critical value for a 95% confidence interval is approximately 1.96.

Plugging in the values into the formula, we get:

Confidence Interval = 32.6 ± 1.96 * (18.2 / sqrt(210))

Calculating the values, we get:

Confidence Interval ≈ 32.6 ± 1.96 * 1.261

Confidence Interval ≈ 32.6 ± 2.469

Therefore, the 95% confidence interval for the mean age at which transgender adults begin transitioning is approximately (30.131, 35.069).