This chapter is from Introduction to Statistics for Community College Students, 1st Edition, by Matt Teachout, College of the Canyons, Santa Clarita, CA, USA, and is licensed

under a “CC-By” Creative Commons Attribution 4.0 International license – 10/1/18

Problem Set Section 1E

1. Convert each of the following percentages into a proportion. Do not round the answers.

a) 75% b) 2.75% c) 0.664% d) 0.082% e) 39.7% f) 8.6% g) 0.189% h) 0.0025% i) 3.16% j) 250% k) 96.1% l) 0.48% m) 0.007% n) 8.73% o) 66.2% p) 9% q) 100%

2. Convert each of the following proportions into a percentage. Do not round the answers.

a) 0.057 b) 0.812 c) 0.0033 d) 0.0214 e) 0.0613 f) 0.451 g) 0.00045 h) 0.0779 i) 0.046 j) 0.3161 k) 0.0027 l) 0.051 m) 0.0058 n) 0.847 o) 1 p) 0.00022 q) 0.0204

(#3-10) Directions: Convert the given percentages into proportions. Then use the following formula to find the estimated amounts. Round your answers to the ones place.

???????????????????????????????????? ???????????????????????? = ???????????????????????????????????????? × ????????????????????

3. According to an article by CBS news, approximately 15% of Americans still do not have health insurance. If approximately 78,300 people live in Chino Hills CA, then how many people in Chino Hills would we expect to not have health insurance? Round your answer to the ones place.

4. According to an article online, about 30% of Americans own at least one gun. About 305,700 people live in Stockton CA. If the article was accurate, then approximately how many people in Stockton do we expect to own at least one gun? Round your answer to the ones place.

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This chapter is from Introduction to Statistics for Community College Students, 1st Edition, by Matt Teachout, College of the Canyons, Santa Clarita, CA, USA, and is licensed

under a “CC-By” Creative Commons Attribution 4.0 International license – 10/1/18

5. An article by the American Diabetes Association estimates that as of 2012, about 9.3% of Americans have diabetes. College of the Canyons has approximately 18,400 students. If the percentage were correct, how many COC students would we expect to have diabetes? Round your answer to the ones place.

6. According to a news report by www.nielsen.com, about 15.9% of Americans struggle with hunger. Lancaster CA has approximately 161,000 people living in it. If the percentage from the Nielsen report is accurate, then how many people in Lancaster CA may be struggling with hunger? Round your answer to the ones place.

7. According to an article by the Autism Society, about 1.47% of people in the U.S. have autism. The article also stated that the percentage is increasing every year and that Autism is one of the fastest growing disorders in the U.S. Van Nuys, CA has approximately 136,400 people living in it. If the percentage by the Autism Society is correct, how many do we expect to have autism?

8. According to a recent article, about 0.51% of airbags in the U.S. are defective. According to vehicle registration data, there are approximately 1,769,000 cars in San Francisco, CA. How many of them do we expect to have defective airbags?

9. According to a recent U.S. census, about 14.8% of people in the U.S. live below the poverty line. About 305,700 people live in Stockton CA. If the census was accurate, then approximately how many people in Stockton are living in poverty?

10. According to an article by the American Medical Association, approximately 33% of medical doctors in the U.S. have been sued by patients for malpractice. Suppose a hospital has currently 147 doctors on staff. How many of them do we expect to have been sued for malpractice?

(#11-15) Directions: Use the following formulas to calculate the proportions, percentages and the percent of increase. Then answer the given questions.

Decimal Proportion = ???????????????????????? ????????????????????

Percentage = Decimal Proportion × 100%

Percent of Increase = (????????????????????? ???????????????????????????????????????? ? ???????????????????? ????????????????????????????????????????)

???????????????????? ???????????????????????????????????????? × 100%

11. An article at www.seattletimes.com was addressing the issue of whether women in the U.S. prefer traditional jeans or athletic wear like yoga pants, sweat pants or leggings. Assume that a random sample of 213 total women were asked if they prefer traditional jeans or athletic wear. Assume 139 said they prefer athletic wear and 74 said they prefer traditional jeans. Calculate the decimal proportions and the percentages for both athletic wear and traditional jeans. Then calculate the percentage of increase. Does the percent of increase look statistically significant? Do you think it is practically significant? Explain.

12. The article at www.seattletimes.com also said that jean companies are creating more and more stretchy jeans to compete with the growing trend of women preferring athletic wear. Assume that a random sample of 197 total women were asked if they prefer stretchy jeans or athletic wear. Assume 103 said they prefer athletic wear and 94 said they prefer stretchy jeans. Calculate the decimal proportions and the percentages for both athletic wear and stretchy jeans. Then calculate the percentage of increase. Does the percent of increase look statistically significant? Do you think it is practically significant? Explain.

13. A hospital is trying to decide how to allocate resources to various departments. In particular, they are comparing the medical/surgical ward to the telemetry (heart monitor) ward since these wards have similar costs per patient. Assume we looked at a random sample of patients admitted to the hospital. Of the 350 total patients, 57 were admitted to the medical/surgical ward and 49 were admitted to telemetry. Calculate the decimal proportions and the percentages for both medical/surgical and telemetry. Then calculate the percentage of increase. Does the percent of increase look statistically significant? Do you think it is practically significant? Explain.

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This chapter is from Introduction to Statistics for Community College Students, 1st Edition, by Matt Teachout, College of the Canyons, Santa Clarita, CA, USA, and is licensed

under a “CC-By” Creative Commons Attribution 4.0 International license – 10/1/18

14. A company found that of their 348 total employees, 96 employees have health insurance and 252 employees do not have health insurance. Calculate the decimal proportions and the percentages for both having health insurance and not having health insurance. Then calculate the percentage of increase. Does the percent of increase look statistically significant? Do you think it is practically significant? Explain.

15. An experiment was done to test the effectiveness of a new medicine to treat depression. They found that of the 57 people that received the medicine, 13 indicated significant improvement in their depression symptoms. Of the 61 people in the placebo group, 11 indicated significant improvement in their depression symptoms. Calculate the decimal proportions and the percentages for the medicine and placebo groups. Then calculate the percentage of increase. Does the percent of increase look statistically significant? Do you think it is practically significant? Explain.

(#16-20) Directions: Go to www.matt-teachout.org, click on the “statistics” tab and then “data sets”. Open the indicated data set and copy the indicated column of categorical data. Go to www.lock5stat.com and click on StatKey. Under the “descriptive statistics and graphs” menu, click on “one categorical variable”. Click on the “edit data” button and paste in the column. Check the box for “raw data” and “data has a header row” and push OK. Then answer the questions. Use the following formula for the percent of increase calculation.

Percent of Increase = (????????????????????? ???????????????????????????????????????? ? ???????????????????? ????????????????????????????????????????)

???????????????????? ???????????????????????????????????????? × 100%

16. Open the “Math 140 Survey Data Fall 2015” at www.matt-teachout.org. Look at the campus data. Use StatKey to make a bar chart, and a summary of the proportions and counts. What proportion of the students went to Valencia? What proportion of the students went to the Canyon Country campus? Calculate the percentage of increase. Does the percent of increase look statistically significant? Do you think it is practically significant? Explain.

17. Open the “Math 140 Survey Data Fall 2015” at www.matt-teachout.org. Look at the gender data. Use StatKey to make a bar chart, and a summary of the proportions and counts. What proportion of the students identified as female? What proportion of the students identified as male? Calculate the percentage of increase. Does the percent of increase look statistically significant? Do you think it is practically significant? Explain.

18. Open the “Math 140 Survey Data Fall 2015” at www.matt-teachout.org. Look at the hair color data. Use StatKey to make a bar chart, and a summary of the proportions and counts. Which hair color had the highest proportion? Which hair color had the lowest proportion?

19. Open the “Math 140 Survey Data Fall 2015” at www.matt-teachout.org. Look at the political part data. Use StatKey to make a bar chart, and a summary of the proportions and counts. What proportion of the students identified as democratic? What proportion of the students identified as republican. Calculate the percentage of increase. Does the percent of increase look statistically significant? Do you think it is practically significant? Explain.

20. Open the “Math 140 Survey Data Fall 2015” at www.matt-teachout.org. Look at the “month of birthday” data. This data has numbers in it. Explain why this is categorical data and not quantitative. Use StatKey to make a bar chart, and a summary of the proportions and counts. Which month had the highest percentage? Which month had the lowest percentage?

(#21-25) Use the following pie charts from Statcato to answer the following questions. Use the following formula for the percent of increase calculation.

Percent of Increase = (????????????????????? ???????????????????????????????????????? ? ???????????????????? ????????????????????????????????????????)

???????????????????? ???????????????????????????????????????? × 100%

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This chapter is from Introduction to Statistics for Community College Students, 1st Edition, by Matt Teachout, College of the Canyons, Santa Clarita, CA, USA, and is licensed

under a “CC-By” Creative Commons Attribution 4.0 International license – 10/1/18

21. The following pie chart was created from the “car data” at www.matt-teachout.org. What percentage of the cars were made in France? How many of the cars were made in the U.S.? What proportion of the cars were made in Sweden? Calculate the percent of increase to compare Japan and Germany. Does the percent of increase look statistically significant? Do you think it is practically significant? Explain.

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http://www.matt-teachout.org/
This chapter is from Introduction to Statistics for Community College Students, 1st Edition, by Matt Teachout, College of the Canyons, Santa Clarita, CA, USA, and is licensed

under a “CC-By” Creative Commons Attribution 4.0 International license – 10/1/18

22. The following pie chart was created from the “car data” at www.matt-teachout.org. What percentage of the cars four cylinders? How many of the cars have eight cylinders? What proportion of the cars six cylinders? Calculate the percent of increase to compare four and eight cylinder cars. Does the percent of increase look statistically significant? Do you think it is practically significant? Explain.

https://creativecommons.org/licenses/by/4.0/
http://www.matt-teachout.org/
This chapter is from Introduction to Statistics for Community College Students, 1st Edition, by Matt Teachout, College of the Canyons, Santa Clarita, CA, USA, and is licensed

under a “CC-By” Creative Commons Attribution 4.0 International license – 10/1/18

23. The following pie chart was created from the “cereal data” at www.matt-teachout.org. What percentage of the cereals did Quaker make? How many of the cereals did Ralston make? What proportion of the cereals did General make? Calculate the percent of increase to compare Kelloggs and Quaker. Does the percent of increase look statistically significant? Do you think it is practically significant? Explain.

https://creativecommons.org/licenses/by/4.0/
http://www.matt-teachout.org/
This chapter is from Introduction to Statistics for Community College Students, 1st Edition, by Matt Teachout, College of the Canyons, Santa Clarita, CA, USA, and is licensed

under a “CC-By” Creative Commons Attribution 4.0 International license – 10/1/18

24. The following pie chart was created from the “cereal data” at www.matt-teachout.org. What percentage of the cereals were targeted toward adults? What percentage of the cereals were targeted toward children? Calculate the percent of increase to compare adult cereals and children cereals. Does the percent of increase look statistically significant? Do you think it is practically significant? Explain.

https://creativecommons.org/licenses/by/4.0/
http://www.matt-teachout.org/
This chapter is from Introduction to Statistics for Community College Students, 1st Edition, by Matt Teachout, College of the Canyons, Santa Clarita, CA, USA, and is licensed

under a “CC-By” Creative Commons Attribution 4.0 International license – 10/1/18

25. The following pie chart was created from the “cereal data” at www.matt-teachout.org. What percentage of the cereals are displayed on the top shelf? How many of the cereals are displayed on the bottom shelf? What proportion of the cereals are displayed on the middle shelf? Calculate the percent of increase to compare the top and bottom shelf cereals. Does the percent of increase look statistically significant? Do you think it is practically significant? Explain.

Optional Binomial Probability Questions

(#26-30) Directions: Open Statcato on either one of the in-class or TLC computers. Go to the “calculate” menu, click on “probability distributions” and then “binomial”. Enter the total under “number of trials” and the proportion under “event probability”. Under “constant” put in the number of successes. Check “probability density” if you want to calculate equal to. Check “cumulative probability” to calculate less than or equal to. For greater than or equal to, subtract your less than or equal to (opposite) answer from one. Assume the questions meet the requirements for calculating a binomial probability.

26. To win at a dice game, the player must role two dice and get a 7 or 11 sum. This game has a 22.2% chance of winning. Suppose a player rolls the dice 18 times.

a) What is the probability that they win exactly once? b) What is the probability that they win two times or less? c) What is the probability that they do not win at all? (This means she wins zero times.) d) What is the probability that they win three times or less? e) What is the probability that they win four or more times? (Subtract your answer in (d) from one.) f) What is the probability that they win four times or less? g) What is the probability that they win five or more times? (Subtract your answer in (f) from one.)

https://creativecommons.org/licenses/by/4.0/
http://www.matt-teachout.org/
This chapter is from Introduction to Statistics for Community College Students, 1st Edition, by Matt Teachout, College of the Canyons, Santa Clarita, CA, USA, and is licensed

under a “CC-By” Creative Commons Attribution 4.0 International license – 10/1/18

27. A car company thinks that their minivan transmissions have a 12% defective rate. A total of 84 minivans were brought in to a service center this month.

a) What is the probability that exactly 11 of them need to have their transmission replaced? b) What is the probability that exactly 8 of them need to have their transmission replaced? c) What is the probability that 12 or less of the minivans will need their transmission replaced? d) What is the probability that 13 or more of the minivans will need their transmission replaced? (Subtract your answer in (c) from one.) e) What is the probability that 6 or less of the minivans will need their transmission replaced? f) What is the probability that 7 or more of the minivans will need their transmission replaced? (Subtract your answer in (e) from one.)

28. Suppose we take a random sample of 57 total people and ask them if they smoke cigarettes or not. Assume that the population percentage for smoking in the U.S. is 15.5%.

a) What is the probability that we will get 9 or less people that smoke in the data set?

b) We need to have at least 10 people in the data set that smoke. What is the probability that we will get 10 or more people that smoke in the data set? (Subtract your answer in part (a) from 1.) Is this percentage high enough for us to be confident that 57 people is a large enough data set? Explain.

29. Suppose we take a random sample of 57 total people and ask them if they smoke cigarettes or not. Assume that the population percentage for non-smokers in the U.S. is 84.5%.

a) What is the probability that we will get 9 or less people that do not smoke in the data set?

b) We need to have at least 10 people in the data set that do not smoke. What is the probability that we will get 10 or more people that smoke in the data set? (Subtract your answer in part (a) from 1.)

30. Suppose a person is playing a game of roulette that has a 2.63% probability of winning. The person plays the game forty times.

a) What is the probability that they do not win at all? (The probability they win zero times.) b) What is the probability that they win exactly one time? c) What is the probability that they win two or less times? d) What is the probability that they win three or more times? (Subtract your answer in (c) from one.) e) What is the probability that they win one or less times? f) What is the probability that they win two or more times? (Subtract your answer in (e) from one.)

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