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.

Answer 1

We can be 95% confident that the true mean age at which transgender adults begin transitioning falls within the range of 30.15 to 35.05 years. This means that if we were to repeat this study multiple times, 95% of the calculated confidence intervals would contain the true mean age of transitioning.

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

Confidence Interval= Xbar ± Z(s/√n)

where:

Xbar is the sample mean age at which transgender adults begin transitioning,s is the standard deviation of the sample,n is the sample size,Z is the Z-score corresponding to the desired confidence level.

Given in the study:

Xbar =32.6,

s=18.2,

n=210.

To find the Z-score for a 95% confidence interval, we consult a standard normal distribution table or use statistical software. For a 95% confidence interval, the Z-score is approximately 1.96.

Now, substitute these values into the formula:

Confidence Interval=32.6±1.96

Calculating the standard error of the mean

Now plug this into the formula:

Confidence Interval=32.6±1.96×1.256

Calculating this, we get a 95% confidence interval of approximately 30.15 to 35.05