Statistics Project

Please follow the directions closely. The credit will not be given if you fail to do so .

The project is due Dec 8 (midnight). It must be uploaded as a pdf file. 25 points will be deducted for each day delayed.

Use data that I provide for you in the Data for the Final Project (also available in Modules on Canvas) and perform three hypotheses testing. The data for Company A is based on a sample randomly selected from its workers. The information about Company B is based on the entire population of workers there so you do not need to test anything about it. It is given to you only to allow you to come up with a more creative claims. One analysis should be testing the mean with the use of normal distribution, one testing the mean using t-distribution, and one testing proportions. All about Company A.

Examples of claims: The proportion of workers with green eyes in Company A is smaller than the one in Company B; The average number of sick days taken by the workers of Company A is 4 (more examples at the bottom of this document).

Select the right data for all analyses (there are a lot of choices for each type of analysis, select any ).

Each analysis should be done in the manner described below (please do follow the scheme otherwise I will not give you any credit). Your work must be done in an orderly and neat way. Please always write full sentences. Use capital letters where they are needed. The way you display your work is always very important.

Here is the scheme you must follow for each of your three analyses (do not change the order, if you do, I will deduct 5 points from each analysis).

1. Write the claim (state it as a sentence). It should be just one sentence, nothing else (for example, average salary in Company A is less than in Company B by $5000).

2. Copy the data that you will be using for your analysis (this means copying part of the data provided, please do not include any calculations).

3. State whether you are testing the mean or proportions. Please write (exactly this, filling in the blank): ”The test of the claim above is testing _______________ (mean, proportion)“.

4. Check if the assumptions of the test that you are about to perform are satisfied (to this end use the following recommendations: Assumptions for Hypothesis Testing).

5.State the null and alternative hypotheses. Use the symbols and conventions that are used in statistics (for example, H0: ρ = 0 HA: ρ ≠ 0 ; use the right symbol for a mean and for proportion; see How to type symbols in Word).

6. State which of the hypotheses is the claim (for example “The claim is the alternative hypothesis”).

7. State what distribution you are going to use (normal or t-distribution with ________ degrees of freedom). Please write (exactly this, filling in the blank): “To test the above hypothesis I am going to use _______________ distribution.”

8. State whether the test is a two-tailed, right-tailed, or left-tailed test. Please write (filling the blank: “This is _____________ test”.

9. Choose the significance level for your test. Please write “α=_____”.

10. As you probably know, the significance level is related to Type I error. Please write one sentence how they are related. Please include that in all analyses (i.e. repeat it each time).

11. If you are testing proportions, write the value of the sample proportion; if you are testing means write the value of sample standard deviation (or population standard deviation). Use the correct symbols and equal signs, like s=4.7 or σ=3.2 (please notice that you can copy the symbols from How to type symbols in Word).

12. Type the formula for the test statistic you are going to use and give its value. Please do not include any calculations and remember to use equal sign and place it where it belongs.

13. Find critical values for your test statistic; Make sure that you include the right signs in front of the value(s) (i.e. plus, minus).

14. Find p-value for your statistic. Write “p-value = ___________”.

15. Write the definition of p-value (please write it as a full sentence, i.e. “P-value is….”. (use capital letters where needed). Repeat this definition in each analysis.

16. Determine if you need to reject or fail to reject the null hypothesis. Please explain the basis for your decision. Write something like “I fail to reject the null hypothesis because p-value is smaller than significance level”.

17. Write your final conclusion. Please follow the instructions below (you can also find them in Formulating final conclusions in hypotheses testing.)

Conclusions are based on the original claim, which may be the null or alternative hypothesis. The decisions are always based on the null hypothesis

	Original Claim
	Original claim contains the condition of equal sign (claim is the null hypothesis)	Original claim contains the condition of equal sign (claim is the alternative hypothesis)
Reject H0	There is sufficientevidence at the alpha level of significance to reject the claim that (insert original claim here)	There is sufficientevidence at the alpha level of significance to support the claim that (insert original claim here)
Fail to reject H0	There is insufficientevidence at the alpha level of significance to reject the claim that (insert original claim here)	There is insufficientevidence at the alpha level of significance to support the claim that (insert original claim here)

Evaluation of the project:

Each analysis is worth 34 points (two points for each “subquestion”).

Information about data:

The data that you see is sample data from Company A. Your goal is to compare it (by using this sample data and performing hypotheses testing) with what we know about Company B (see below)

We know the following about Company A:

population standard deviation of number of sick days taken in 2017 is 1

population standard deviation of number of vacation taken is 10

population standard deviation of number of kids for each worker is 0.5

We know the following about Company B:

average age is 25

proportion of workers with college is 0.4

workers with green eyes is 0.2 with hazel 0.3 with black 0.5 and blue eyes is 0.1

average # of kids is 1.2

proportion of workers without kids is 0.3

average weight id 145

average height 175cm

proportion of democrats 0.6, republicans 0,4 (no independents)

average salary $55000

proportion of workers owning a house 0.6, owning a car 0.8

average of days of vacation taken in 2017 10.9; sick days taken 2

average of years in company 4.

Examples of claims (once again)

• Proportion of workers in Company A having their own house is equal to the proportion of such workers in Company B.
• Average salary in Company A is greater than in Company B.