Analyze the provided data to determine the total sample size, identify the independent and dependent variables, and describe the relationship between the independent and dependent variables.

The text states: "A group of 20 women from each age group... were selected randomly."

From the graph, the age groups are 22, 28, 34, 40, and 46. There are 5 age groups.

Total sample size = (Number of women per group) $\times$ (Number of age groups)

The sample size selected for this investigation was $\boxed{\text{100 women}}$.

3.1.2

a) Independent variable
The independent variable is the factor that is changed or controlled by the experimenter. In this investigation, the age of women is being varied to observe its effect.
The independent variable is $\boxed{\text{Age of women}}$.

b) Dependent variable
The dependent variable is the factor that is measured or observed in response to changes in the independent variable. Here, the chances or incidence of miscarriages are being measured.
The dependent variable is $\boxed{\text{Chances of miscarriages (or Incidence of miscarriages)}}$.

3.1.3

As the age of women increases (from 22 to 46), the incidence of miscarriages also increases.
At age 22, the incidence is 10%.
At age 28, the incidence is 11%.
At age 34, the incidence is 15%.
At age 40, the incidence is 24%.
At age 46, the incidence is 50%.

There is a positive correlation between the age of women and the chances of miscarrying. As women get older, the likelihood of them experiencing a miscarriage increases.

3.1.4

To improve the reliability of this investigation, one could:

• Increase the sample size: Using a larger number of women in each age group would make the results more representative and less prone to random variation.
• Repeat the investigation: Conducting the study multiple times with different samples could help confirm the consistency of the findings.
• Standardize conditions: Ensure that all other factors (medical care, physical activities, social environment) are as consistent as possible across all groups to isolate the effect of age.

3.1.5

For women aged 46, the incidence of miscarriages is 50%.

The text states: "A group of 20 women from each age group... were selected randomly." So, there are 20 women in the 46-year-old group.

According to the data, $\boxed{\text{10}}$ of the women sampled who are 46 years old are likely to miscarry.