MATH309 – Statistics Week 7 – Homework

For this assignment, please review the linked videos and worked examples within this document. Answer each question below from provided material into a Word File. You will copy all your work from Excel into a single Word document.  You will submit your Word document with your homework answers AND submit your Excel spreadsheet to show the work.

Expected Value – [20 points]

A survey conducted at one particular high school in the month of December gives the following table.

The percentage of students that watched 1 movie is 17%. If we assume that the students at this high school are typical, the we could say that the probability that a high school student will watch 1 movie is 17% or 0.17.  Notice that the percentages or probabilities add to 1 or 100%.

Example: The expected value would be the average value of the table above. We calculate this by multiplying each number by its percentage and adding them together.

E(x) = 1*(0.17) + 2*(0.28) + 3*(0.34) + 4*(0.15) + 5*(0.06)

= 0.17 + 0.56 + 1.02 + 0.90 + 0.30

= 2.95

We expect the average high school student to watch 2.95 movies per month.

Example: A local club plans to invest $10000 to host a baseball game. They expect to sell enough tickets to make a profit of $5000 per game. But, if it rains, they won’t sell any tickets and the club will lose all the money invested. If the weather predicts a 20% chance of rain, is this a good investment?

We can write our probability distribution like this:

Find the expected value of the money earned in this investment. We find the expected value of the probability distribution.

E(x) = 5000(0.8) – 10000(0.20)

= 4000 – 2000

= 2000

The club can expect a return of $2000 on their investment.

• Several college students were asked how many medications they take on a daily basis. The results are in the table below:

Find the expected value of the number of medications. How would we interpret this expected value result?

• A capital company plans to invest in a company. Company A has a 30% chance of earning a profit of $90,000 and a 70% chance of a -10,000 loss. Find the expected value of this investment. Do you think this would be a wise investment?

Find the expected value of the money earned in this investment. How would we interpret this expected value result?

Additional Video to Review Material on Expected Value

Expected Value of discrete random variable: Mean (Expected Value) of a Discrete Random Variable

Learning the Material – Chi-Square Tests [30 points]

Watch the following instructional video on the Chi-square Test. Then, answer the following questions.

Analyzing Data in a Two-Way Table (Including Chi-Squared Test)

• The Chi-square test of independence is used on what type of data (What is the level of measurement of the variables)?

• According to the video, if we want to graphically represent the data from a Two-way table, which graph could we use?

• Write out null and alternative hypothesis for Helen’s Chi-square test comparing gender and chocolate preference.

Application of the Material – Run a Chi-Square Test [50 points]

Watch the following video explains how to run a Chi-square test in Excel.

Performing a Chi Squared Test in Excel

Problem: In 2017, Pew Research Center did a research study to see if men and women thought gender discrimination is a problem in the tech industry. Survey participants were asked “Discrimination against women is a (major problem/minor problem) in the tech industry”. The results of the survey by gender are found in Table 1. The researchers want to know if gender and severity of discrimination are associated. Conduct a Chi-square Test with the data below in Table 1. You will use the same 5 step process for conducting a Hypothesis Test.

Step 1: Write out the Hypotheses for this test

Null hypothesis:

Alternative hypothesis:

Step 2: Significance level

Choose the standard significance level 0.05.

Step 3: Collect a Sample

The data for Hypothesis Test can be found in Table 1. Enter the data into Excel. Complete the Totals Column and Row and Paste your data table below with the completed Total columns. You can use the =sum( ) function in Excel.

Table 1: Do you see Gender Discrimination as a major problem in the Tech Industry?

Observed Frequencies (Fill in the Total column and row)

Step 4: Find the Expected Values of the 2-way table and calculate a p-value

Question 1: What are the calculated expected values of the Two-way table? Complete the table below.

Expected Frequencies (Fill in the expected values and the total row and total column)

Question 2: What is the p-value of the Chi-square test?

Step 5: Decide – What decision do you make regarding the null hypothesis? How do you interpret the association between gender and severity of gender discrimination in the tech industry?