Construct a 95% confidence interval for the mean difference between the average age of a smoker, and the average age of a non-smoker. variables smokers = SMQ020 age = RIDAGEYR use the next libraries if are required: import matplotlib.pyplot as plt import pandas as pd import numpy as np import seaborn as sns import statsmodels.api as sm

To construct a 95% confidence interval for the mean difference between the average age of a smoker and a non-smoker, we will use the `statsmodels` library in Python. We will assume that you have a pandas DataFrame `df` with the data.

```python
import pandas as pd
import numpy as np
from statsmodels.formula.api import ols
from statsmodels.stats.anova import anova_lm
import statsmodels.api as sm

# Assuming df is your DataFrame
# Define the model
model = ols('RIDAGEYR ~ C(SMQ020)', data=df).fit()

# Print the summary of the model
print(model.summary())

# Get the coefficients
coefficients = model.params

# Get the standard error of the coefficient
std_error = model.bse[1]

# Calculate the standard error of the mean difference
std_error_mean_diff = std_error * np.sqrt(1 + 1/len(df[df['SMQ020'] == 1]) + 1/len(df[df['SMQ020'] == 0]))

# Calculate the standard error of the mean difference for the two groups
std_error_group1 = std_error * np.sqrt(1 + 1/len(df[df['SMQ020'] == 1]))
std_error_group2 = std_error * np.sqrt(1 + 1/len(df[df['SMQ020'] == 0]))

# Calculate the t-statistic
t_statistic = coefficients[1] / std_error_mean_diff

# Calculate the degrees of freedom
df = len(df) - 2

# Calculate the critical t-value for a 95% confidence interval
critical_t_value = 2.045  # This is the critical t-value for a two-tailed test with 98 degrees of freedom and a 5% significance level

# Calculate the margin of error
margin_of_error = critical_t_value * std_error_mean_diff

# Calculate the 95% confidence interval
lower_bound = coefficients[1] - margin_of_error
upper_bound = coefficients[1] + margin_of_error

print(f'95% Confidence Interval: ({lower_bound}, {upper_bound})')
```

This code will calculate the 95% confidence interval for the mean difference between the average age of a smoker and a non-smoker. The interval is calculated using the formula for a two-sample t-test.

Note: The critical t-value used in this code is for a two-tailed test with 98 degrees of freedom and a 5% significance level. If you want to use a different significance level or number of degrees of freedom, you will need to look up the corresponding critical t-value.

Also, note that this code assumes that the data is normally distributed and that the variances of the two groups are equal. If these assumptions are not met, you may need to use a different method to calculate the confidence interval.