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_Wheel_Chisquare_Q2.xlsx

M11_BloodPressure_Age_Chisquare_Q5.xlsx

Instructions

Part A

Complete the following:

1. 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)
2. 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

3. 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

4. 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

5. 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.

1. 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)
2. 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)
3. 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)