A study of two groups of children since early childhood:
One group of 62 attended preschool.
A control group of 61 children from the same area and similar backgrounds did not attend preschool.
Over 10 year period as adults, 38 of the preschool sample and 49 of the control sample needed social services.
A. Does the study provide significant evidence that children who attend preschool have less need for social services as adults?
B. How large is the difference between the proportions of the preschool and no-preschool populations that require social services?
C. Do inference to answer both questions.
Be sure to explain exactly what inference you choose to do.
Please help me with the set up for all three parts to get started. Thanks
To answer the questions using inference, we can perform a hypothesis test and calculate a confidence interval. Here's how we can set up each part:
A. To determine if the study provides significant evidence that children who attend preschool have less need for social services as adults, we can set up a hypothesis test.
Null Hypothesis (H0): There is no difference between the proportions of the preschool and no-preschool populations that require social services.
Alternative Hypothesis (H1): Children who attend preschool have less need for social services as adults.
We can use a two-proportion z-test to compare the proportions in the two groups. We'll calculate the test statistic and the p-value to assess the significance level.
B. To determine the size of the difference between the proportions of the preschool and no-preschool populations that require social services, we can calculate a confidence interval.
We'll calculate a confidence interval for the difference in proportions. This will give us an estimate of the range within which the true difference lies.
C. To answer both questions, we'll perform the inference using the approach described above and interpret the results obtained from the hypothesis test and confidence interval calculations.
Now that we have the set up for all three parts, we can proceed with calculations and interpretations in the following steps.