Hypothesis Testing is the use of statistics to determine the probability that a given claim is true.
In Part II of this project, you will choose a data set, review claims and perform hypothesis testing and make a decision. You will then complete a write-up that includes the calculations.
The government logs the number of documented births, deaths, marriages and divorces however it is possible to have undocumented cases. In part II of this project, you are going to test claims about total births, deaths, marriages and divorces.
- Choose a Data Set.
- Go to https://www.cdc.gov/nchs/products/nvsr.htm (Links to an external site.)
- In the search bar type: Births, Marriages, Divorces, and Deaths
- Pick a DataSet and download the PDF document and make note of the volume, number, and date. For example,
- Pick the same month/year combination for each data set. For example, choosing September of 2009.
- Preliminary Calculations
- Create a summary table for 1. Live Births, 2. Deaths, 3. Marriages, and 4. Divorces highlighting the mean, median, sample/population standard deviation, n = number of states that submitted data for each the data sets. You will have FOUR tables using the list of values of each state, the District of Columbia and Puerto Rico (You could have 52 numbers for each data set. You may have less data numbers if not all states/territories submitted data values.)
| Summary Table for _________ | |
| Mean | |
| Median | |
| Standard Deviation | |
| n (Number of States who submitted Data) | |
- Hypothesis Testing
With the information that you gather from the summary tables, test the following (you can use excel when appropriate):
- Determine if there is sufficient evidence to conclude the average amount of births is over 5000 in the United States and territories at the 0.05 level of significance.
- Determine if there is sufficient evidence to conclude the average amount of deaths is equal to 6000 in the United States and territories at the 0.10 level of significance.
- Determine if there is sufficient evidence to conclude the average amount of marriages is greater or equal to 2500 in the United States and territories at the .05 level of significance.
- Determine if there is sufficient evidence to conclude the average amount of divorces is less than or equal to 4000 in the United States and territories at the 0.10 level of significance.
For each of the tests above, in your report, be sure to—
- Clearly state a null and alternative hypothesis
- Give the value of the test statistic
- Report the P-Value
- Clearly state your conclusion (Reject the Null or Fail to Reject the Null)
- Explain what your conclusion means in context of the data.
4. Make your OWN Claim (You are completing ONE more Hypothesis Test)
Lastly, propose and conduct your own test of hypothesis.
a) Pick one data set: Births, Deaths, Marriages OR Divorces.
b) Write a claim about the data set.
c) For your claim—
- Clearly state a null and alternative hypothesis
- Give the value of the test statistic
- Report the P-Value
- Clearly state your conclusion (Reject the Null or Fail to Reject the Null)
- Explain what your conclusion means in context of the data.
ANSWER:
Births, marriages, divorces, and deaths: Provisional data for September 2009
….
Hypothesis Testing
- Determine if there is sufficient evidence to conclude the average amount of births is over 5000 in the United States and territories at the 0.05 level of significance.
The sample size of the dataset (n) = 52
The sample mean of the dataset = 7047
The sample standard deviation (s) = 8358
The null and alternative hypotheses are as follows;
Null hypothesis, H0:u=5000
Alternative hypotheses Ha:u>5000
Test statistic is given by Z= (x – μ0)/(σ/√n)= 1.77
The critical value at 0.05 level of significance is, Z* = 1.645 … To continue reading, click on the button below.