Question

The dataset that we will investigate is Public Health Statistics for the City of Chicago by neighborhood which represents the years 2005-2011. The data contains 27 variables with measures such as death rates, birthrates, Assault, Breast Cancer, Diabetes, per Capita Income and many other measures. The dataset represents 77 area (neighborhoods) in the City of Chicago which we will treat as individual observations n=77 as it has been estimated through different sampling methods and sources. The data is provided by the department of Public Health and the U.S Census Bureau.

1. Look through the data set and the different variables provided. Why would the City of Chicago care about collecting such information for its residents? Explain.

2. For the variable Per Capita Income for all neighborhoods create a histogram with minimum five classes.

3. Describe the Shape of the histogram that you created for the variable per Capita Income.

4. Calculate the five-number summary for the variable Per Capita Income, and represent it using a box plot.

5. In detail, summarize what the information that a five-number summary for the variable Per Capita Income provides for the City of Chicago.

6. Calculate the Mean and Standard deviation for the variable Per Capita Income.

7. Calculate the margin of error for a 95% confidence interval for the mean of the variable Per Capita Income.

8. Determine the 95% Confidence Interval for the mean of the variable Per Capita Income.

9. Interpret the 95% Confidence Interval for the mean of Per Capita Income.

10. A researcher claims that the mean rate of individuals below poverty in the City of Chicago is below 17 %. Based on the data represented for the years 2005 – 2011, perform a hypothesis test to test his claim using a significance level of α = 0.10.

11. Would your conclusion change for question 10 if you used a significance level of α = 0.05? Explain.

12. A survey conducted at Chicago Public Schools (CPS) involving high school students on whether they had participated in binged drinking during the past month. Binge drinking was defined as 5 or more drinks in a row on one or more of the past 30 days.

Number who identified as having participated in Binge Drinking.	72
Total participants	567

a. From the sample data is there evidence that the proportion of students who participate in binge drinking is greater than 10%? Write a null and alternative hypothesis and perform an appropriate significance test using α=0.05.

b. Construct a 90% Confidence Interval for the population proportion. Does it support the same conclusion as in 12a? Explain.

Answer 1

Only 12 can be solved as the data for the previous question is not provided.

a. From the sample data is there evidence that the proportion of students who participate in binge drinking is greater than 10%? Write a null and alternative hypothesis and perform an appropriate significance test using α=0.05.

Ho: proportion of students who participate in binge drinking is equal 10%
H1 : proportion of students who participate in binge drinking is greater than 10%

There is sufficient to support the claim that the proportion of students who participate in binge drinking is greater than 10%

b. Construct a 90% Confidence Interval for the population proportion. Does it support the same conclusion as in 12a? Explain.

Yes it support the same conclusion since the 90% confidence interval which is (0.104,0.15) is contains 0.10 and is greater than 0.10, indicating that the proportion is greater than 0.10.