This weekend please complete the "Inference for Two Proportions" worksheet provided in class--this homework is a summary of what we need to know about chapter 22 for our test! Put in max effort!
Here are the questions in case you lost your paper or were out:
Inference for Two Proportions
1.) Among
242 Cleveland-area children born prematurely at low birth weights between 1977
and 1979, only 74% graduated from high school. Among a comparison group of 233
children of normal birth weight, 83% were high school graduates.
a.) Verify that the conditions for a 2 Proportion Z Interval
are met. (4 points)
b.) Create a 95% confidence interval to estimate the difference in graduation rates between children of
normal and very low birth weights. Show the appropriate formula and interval
below. (5 points)
c.) Interpret the meaning of your interval, in context. (5
points)
d.) Based on your interval above, do you believe there is a
significant difference in the proportion of normal and low birth weight babies
who graduate? Explain your reasoning. (3 points)
2.) Using an appropriate hypothesis test, determine if there is a statistically
significant difference between graduation rates of normal and low birth weight
babies. Test the hypotheses at the 10% significance level. (We’ll skip the
conditions since they’ve been checked above).
i.)
State your null and alternative hypotheses, using appropriate notation. (2
points)
ii.) Find the z-score and then your p-value. Show a
shaded Normal model, as well as the appropriate z-score formula. (4 points)
iii.) Is there statistically
significant difference between graduation rates of normal and low birth weight
babies? Use your p-value to write your conclusion below. (5(4 points) points)
3. Among 242 Cleveland-area children born prematurely at low
birth weights between 1977 and 1979, only 74% graduated from high school. Among
a comparison group of 233 children of normal birth weight, 83% were high school
graduates. Researchers plan to determine if there is a statistically
significant difference between graduation rates of normal and low birth weight
babies; if there is, schools will provide costly additional educational resources
and support for the low birth weight students. If not, no support will be
provided.
a.) Based on this scenario regarding premature children,
explain what a Type I error would be and name one consequence. (4 points)
b.) Based on this scenario regarding premature children,
explain what a Type 2 error would be and name one consequence. (4 points)
This homework assignment has us studying for the "math" portion of our
test on Tuesday! Start studying your vocab too! Here's the list--if a word was not on a previous vocab quiz the definition is provided:
- Confidence Interval
- Hypothesis Test
- Critical Value
- Standard Error
- Margin of Error
- Confidence Level
- Null Hypothesis
- Alternative Hypothesis
- Standardized Test Statistic
- P-Value
- Alpha level (know 2 definitions)
- Beta
- Reject the null hypothesis (for what types of p-values?)
- Fail to reject the null hypothesis (for what types of p-values?)
- One tailed test (a test that aims to show an increase or decrease in a parameter)
- Two tailed test (a test that aims to show a difference or change in a parameter)
- Type 1 Error
- Type 2 Error
- Power
- Pooling (when we combine our sample data (from both samples) to calculate an overall proportion)
And finally, e sure to sign up for our MANDATORY SATURDAY SESSION on APRIL 1st! The sign up sheet is in the back of the classroom!
- We're using this time as another class, so we'll be learning new stuff!
- We'll do some new learning and some practice in this time...
- You can also sign up for April 22nd, but you don't have to yet...
- Remember, the April vacation session is not mandatory...we'll talk more about that as we get closer...
- You will have a take home test over April break; the review session will be an opportunity to come in and work on your take home test in groups and ask me any questions you might have!
