Math 075

Mod 5 Review 1KEY

Year in College / Cola Pref / Gender
3 : junior / coke / male
1 : freshman / coke / female
1 : freshman / coke / female
1 : freshman / coke / female
5 : other / Pepsi / female
3 : junior / coke / female
1 : freshman / coke / male
2 : sophomore / coke / male
1 : freshman / Pepsi / female
1 : freshman / Pepsi / female
3 : junior / coke / female
2 : sophomore / coke / female
1 : freshman / coke / female
1 : freshman / coke / female
1 : freshman / coke / female
1 : freshman / coke / female
1 : freshman / coke / female
3 : junior / coke / male
3 : junior / coke / female
2 : sophomore / coke / female
1 : freshman / coke / male
1 : freshman / coke / female
2 : sophomore / Pepsi / male
3 : junior / coke / male
3 : junior / coke / male
3 : junior / Pepsi / male
3 : junior / Pepsi / male
1 : freshman / coke / female
2 : sophomore / coke / male
3 : junior / Pepsi / female
1 : freshman / coke / female

6. What percent of freshmen prefer pepsi? What percent of freshmen prefer coke? pepsi: 2/15=13.3%;

coke13/15=86.7%

7. According to these results, does it appear that there is a significant difference between the two groups? Yes, the difference is about 74%. According to this sample, freshmen preferred coke.

Making two way Tables from Percentages

8. A 1969 study among the Pima Indians of Arizona investigated the relationship between a mother’s diabetic status and the appearance of birth defects in her children. Approximately 1000 mothers are represented in the two way table. 5% of the children had one or more birth defects. 6% of those studied had diabetes. Of those who were diabetic, 18% of the children were born with one or more birth defects. Fill in the following table.

Diabetic / Not diabetic / Totals
One or more birth defects / 11 / 39 / 50
None / 49 / 901 / 950
Totals / 60 / 940 / 1000

9. Using the above table, answer the following question: Are mothers with diabetes more likely to have a child with birth defects? Use data to support your answer:

We are told that 50 men and women are polled. They were asked if they had danced, played sports, or watched TV last Friday night. 16 people watched TV. 40% of the people polled were men. 53% of the women said they went dancing. 50% of the men had played sports, and 10% of the men went dancing. Fill in the table below.

Dance / Sports / TV / Total
Men / 2 / 10 / 8 / 20
Women / 16 / 6 / 8 / 30
Total / 18 / 16 / 16 / 50

11. Does one particular gender prefer sports? Men: 10/20=50.0% Women: 6/30=20.0% Yes, the difference is 30%. Men are (50/20 = 2.5) 2.5 times more likely to prefer sports compared to women.

12. Does one particular gender prefer tv?Men: 8/20=40.0% Women: 8/30=26.7%No, the difference is about 13%. There is no significant gender difference in preference in preferring to watch tv. (40/26.7=1.5, 1.5 times more likely; not as significant. I would recommend as least 2 times more likely for there to be a significant difference.)

Reading and Analyzing TwoWay Tables

13. What is the relationship between type of music played in supermarkets and type of wine purchased? Use percentages rounded to the nearest tenth of a percent.

  1. What percentage of the wine bought was French?40.7% (99/243)
  2. Given that Italian music was played, what is the probability that Italian wine was bought?

22.6% (19/84)

  1. What is the probability that the person bought French wine AND was in a supermarket that was playing French music?16.0% (39/243)
  2. What is the probability that wine was bought when music was played?65.4% (159/243)
  3. What is the probability that the wine bought was French OR that French music was played?One way: (99/243) + (75/243) – (39/243) = 55.6%

14. After taking a poll of 229 people, we made the following two way table. Answer the questions and use percentages rounded to the nearest tenth of a percent.

  1. What percent of those polled considers themselves to be a Democrat? 32.3% (74/229)
  2. If a person is male, what is the probability that they are independent?20.4% (22/108)
  3. Given that they are Independent, what is the probability that they are male? 47.8% (22/46)
  4. What is the probability that a person is either Republican or Democratic?57.6% (132/229)
  5. What is the probability that the person picked is female OR independent? 62.4% = (121/229) + (46/229) – (24/229)
  6. What is the probability that the person is female AND independent?10.5% (24/229)
  7. Given that the person is Republican, what is the percentage that they are male?50.0% (29/58)
  8. Write the probability statement that gives the probability of : P(Male | Democrat)

15. Write the sample space of the following experiment: You roll a six sided die, and flip a coin.

{1H,1T,2H,2T,3H,3T,4H,4T,5H,5T,6H,6T}

16. Make a two way table based on the following data on a local little league team. They lost 20% of the games. 30% of thegames they lost were when it was sunny, and 60% of the games were overcast when they won.

a. Two way table:

Sunny / Overcast
Win / 32 / 48 / 80
Lost / 6 / 14 / 20
38 / 62 / 100

b. Given that it was sunny, what is the probability that the team won? 32/38=84.2%

c. Given that it was overcast, what is the probability that the team lost? 48/62=77.4%

d. According to the above statistics, does it appear that

weather contributed to the outcome of a win? Explain.

No, the difference is only about 7%. The weather did not affect the outcome of a win/loss. (The ratio is only 84.2/77.4 = 1.1 times more likely to win when sunny.)

17. You randomly choose a card from a deck of cards. Find the following

probabilities in reduced fraction form and then give the percentages.

  1. Find the probability of picking an Ace1/13=7.7%
  2. Find the probability of picking an Ace AND Spade1/52=1.9%
  3. Find the probability of picking an Ace OR Spade

4/52 + 13/52 – 1/52 = 16/52 = 4/13=30.8%

  1. Find the probability of picking a Queen OR King

4/52 + 4/52 = 8/52 = 2/13=15.4%

  1. Find the probability of picking a face card3/13=23.1%