# 11.8 Assignment 11

## Purposes

This assignment has two parts. The first part assesses your knowledge of conducting a chi-square goodness-of-fit test and performing a chi-square independence test using the chi-square table. The second part assesses your skills in using R commander to conduct a chi-square goodness-of-fit and chi-square independence tests.

## Resources

M11_BloodPressure_Age_Chisquare_Q5.xlsx

## Instructions

**Part A**

Complete the following:

- The
*t*-table has entries for areas of 0.10, 0.05, 0.025, 0.01, and 0.005. In contrast, the [latex]\chi^{2}[/latex]-table has entries for those areas and for 0.995, 0.99, 0.975, 0.95, and 0.90. Explain why the*t*-values corresponding to these additional areas can be obtained from the existing*t*-table but must be provided explicitly in the [latex]\chi^{2}[/latex]-table. (3 marks) - An American roulette wheel contains 18 red numbers, 18 black numbers, and 2 green numbers. The following table shows the frequency with which the ball landed on each colour in 300 trials. At the 5% significance level, do the data suggest that the wheel is out of balance? (10 marks)

**Color**Red Black Green **Frequency**140 120 40 - A gambler thinks a die may not be landed on the six numbers with equal chance. To test his suspicion, he rolled the die 150 times and obtained the data in the following table. Test at the 1% significance level whether the die is balanced. (10 marks)

**Number**1 2 3 4 5 6 **Frequency**23 26 23 21 31 26 - The following table reported the survey results on how members would prefer to receive ballots in annual elections. At the 5% significance level, do the data provide sufficient evidence to conclude that gender (column) and preference (row) are associated? (10 marks)

**Male****Female****Total****Mail**60 30 90 **Email**150 90 240 **Both**70 40 110 **N/A**80 50 130 **Total**360 210 570 - The following table summarizes the age (column) and blood pressure (BP; row) status of 474 randomly selected Canadian adults in 2017. At the 10% significance level, do the data provide sufficient evidence to conclude that age and blood pressure are associated? (10 marks)

**Under 30****30-49****Over 50****Total****High BP**23 51 73 147 **Normal BP**48 91 93 232 **Low BP**27 37 31 95 **Total**98 179 197 474

**Part B**

**Finish the following questions using R and R commander. Make sure that you copy and paste the computer outputs as required, and write down your answers in statements.**

- Refer to Question 2 in Part A. The data are provided in the data file
**M11_Wheel_Chisquare_Q2.xlsx**. Import the data into R commander. Re-conduct the test in Question 2 using R commander. Make sure to include all the six components of a hypothesis test. Copy and paste the computer output first and then compare the answer with the one you obtained by hand in Question 2. (5 marks) - Refer to Question 4 in Part A. Input the two-way table into R commander and conduct a chi-square test using R commander. Make sure to include all the six components of a hypothesis test. Copy and paste the computer output first and then Compare the answer with the one you obtained by hand in Question 4 in Part A. (6 marks)
- Refer to Question 5 in Part A. The data are provided in the data file
**M11_BloodPressure_Age_Chisquare_Q5**.**xlsx**. Import the data into R commander. Re-conduct the test in Question 5 using R commander. Make sure to include all the six components of a hypothesis test. Copy and paste the computer output first and then compare the answer with the one you obtained by hand in Question 2. (6 marks)