# 1 - Los Angeles Mission College

Test 1A

1. Two major branches of statistics are (4pts)

2. A study that involves no researcher intervention is called (4pts)

3. The group of subjects selected from the group of all subjects under study is called a(n) (4pts)

4. If all possible samples of a specific size have the same chance of being selected, what type of sampling technique is being used? (4pts)

5. The survey question "Since everybody likes baseball, you support the construction of the new ball field, don't you?" is a poor survey question because it is (4pts)

|6. |Given the following frequency distribution, how many pieces of data were greater than 28.5? (4pts) |

| |Class Boundaries |

| |Frequencies |

| | |

| |13.5–18.5 |

| |4 |

| | |

| |18.5–23.5 |

| |9 |

| | |

| |23.5–28.5 |

| |12 |

| | |

| |28.5–33.5 |

| |15 |

| | |

| |33.5–38.5 |

| |17 |

| | |

| | |

|7. |Draw a scatter plot for the data given below (8pts) |

| | |

| |x values |

| |9 |

| |8 |

| |5 |

| |5 |

| |12 |

| | |

| |y values |

| |2 |

| |2 |

| |4 |

| |6 |

| |6 |

| | |

|8. |Using the following frequency distribution, construct a frequency polygon. |

| |(MD 5 pts, Graph 5 pts) |

| | |

| |Temperature |

| |Frequency |

| |Mid Point |

| | |

| |28.5–31.5 |

| |1 |

| | |

| | |

| |31.5–34.5 |

| |3 |

| | |

| | |

| |34.5–37.5 |

| |6 |

| | |

| | |

| |37.5–40.5 |

| |10 |

| | |

| | |

| |40.5–43.5 |

| |8 |

| | |

| | |

| |43.5–46.5 |

| |7 |

| | |

| | |

|9. |Given the following two sets of data, draw a stem and leaf plot. (8pts) |

| |22, 22, 24, 34, 31, 26, 35, 27, 49, 10, 45, 23, 16, 28, 18, 13, 10, 30, 31 |

|10. |Construct a Pareto chart for the following distribution: (8pts) |

| |Year in School |

| |Number of Students |

| | |

| |Freshmen |

| |17 |

| | |

| |Sophomores |

| |44 |

| | |

| |Juniors |

| |15 |

| | |

| |Seniors |

| |27 |

| | |

| | |

|11. |The data represent the personal consumption (in billions of dollars) for tobacco in US. Draw a time series graph for the data |

| |and explain the trend. (8pts) |

| |Year |

| |1995 |

| |1996 |

| |1997 |

| |1998 |

| |1999 |

| |2000 |

| |2001 |

| |2002 |

| | |

| |Amount |

| |8.5 |

| |8.7 |

| |9.0 |

| |9.3 |

| |9.6 |

| |9.9 |

| |10.2 |

| |10.4 |

| | |

|12. |Construct a pie graph using the following data from the local bakery. (Degree 5 pts, Graph 5 pts) |

| | |

| |Cookie Types |

| |Number Sold |

| |Degree |

| | |

| |Chocolate Chip |

| |20 |

| | |

| | |

| |Peanut Butter |

| |15 |

| | |

| | |

| |Oatmeal |

| |30 |

| | |

| | |

| |Sugar |

| |10 |

| | |

| | |

[pic]

|13. |What kind of relationship does the scatter plot show between x and y?: (5 pts) |

| | |

| |[pic] |

14. The number of calories per serving for selected cereals is listed below. Construct a frequency destruction using seven classes. (10 pts)

|130 |190 |140 |80 |100 |

|80-107 | |8 | | |

|108-135 | |13 | | |

|136-163 | |2 | | |

|164-191 | |9 | | |

|192-219 | |8 | | |

|220-247 | |4 | | |

|248-275 | |2 | | |

15. Construct a histogram, for the data in Exercise 14 in this section, and analyze the results. (7 pts)

16. Construct an ogive by using the data in Exercise 14 in this section, and analyze the results. (7 pts)

Test 2A

1. A student and a professor each choose a number between 1 and 7 (1 and 7 are both possible choices). What is the probability that the two choose the same number? (3 pts)

2. Evaluate: 9P4 (3 pts)

3. Evaluate: 7C3 (3 pts)

4. A store manager wants to display 9 different brands of toothpaste in a row. How many ways can this be done? (3 pts)

5. Find the mean, mode, median, and midrange value for the following data set.

(10 pts)

10, 17, 18, 18, 17, 22, 17, 30, 12

6. Eighty randomly selected light bulbs were tested to determine their lifetimes. This frequency distribution was obtained. Find the modal class. (3 pts)

|Class Boundries |Xm |f |fXm |

|52.5-63.5 |58 |6 |348 |

|63.5-74.5 |69 |12 |828 |

|74.5-85.5 | 80 |25 | 2000 |

|85.5-96.5 | 91 |18 | 1638 |

|96.5-107.5 |102 |14 | 1428 |

|107.5-118.5 |113 |5 | 565 |

7. Make a boxplot for the following data set. (8 pts)

8, 12, 32, 6, 27, 19, 54

8. If a student scored 17 points on a test where the mean score was 31 and the standard deviation was -5. Then what was the student's z-score? (7 pts)

9. If the mean of a set of data is 22, and 6 has a z-score of –2.00, then what is the standard deviation? (7 pts)

10. Given that the mean of a set of data is 34 and the standard deviation is 3, what would be the coefficient of variation? (4 pts)

11. If a set of data has 49 points and variance 9, then what is the standard deviation? . (4 pts)

12. Given nine students, four of which are females, if two students are selected at random, without replacement, what is the probability that both students are female? (8 pts)

13. If five cards are drawn from a deck of cards without replacement, what is the probability that at least one of the cards is a heart? (8 pts)

14. Three cable channels (6, 8, & 10) have quiz show, comedies and dramas. The number of each is shown here. (10 pts)

|Type of show |Channel 6 |Channel 8 |Channel 10 |

|Quiz show |5 |2 |1 |

|Comedy |3 |2 |8 |

|Drama |4 |4 |2 |

a. The show is a quiz show, or it’s shown on channel 8

b. The show is NOT a Drama on Channel 6.

15. There are 30 blue balls, 45 red balls, and 20 white balls in a bag of balls. What is the conditional probability of choosing a blue ball, given that a white ball was not chosen? (8 pts)

16. A single card is drawn from a deck. Find the probability of selecting a diamond or a king or queen. (8 pts)

17. It two dice are rolled one time, find the probability of getting a sum of 7 or 11. . (8 pts)

Test 3A

1. Find the mean & variance of the distribution shown. (6 pts)

|x |1 |3 |5 |

|P(x) |0.36 |0.40 |0.24 |

2. There are 50,000 people at a stadium watching a soccer match, and 40,000 of them are male. If 3 people are chosen at random, what is the probability that all 3 of them are male? (6 pts)

3. What is the standard deviation of the following probability distribution? (4 pts)

|x |1 |2 |4 |6 |8 |

|P(x) |0.2 |0.05 |0.35 |0.25 |0.15 |

4. A market research company found that 40% if Americans do not think that having a college education is important to succeed in the business world. If a random sample of five Americans is selected, find the possibility that fewer than two people will agree. (10 pts)

5. For the following data, construct a graph showing the probability distribution. . (4 pts)

|x |0 |1 |2 |3 |4 |

|P(x) |0.12 |0.24 |0.12 |0.28 |0.24 |

6. A bank vice president feels that each saving account customer has, on average, three credit cards. The following distribution represents the number of credit cards people owns. Find the standard deviation. (4 pts)

|Number of cards X |0 |1 |2 |3 |4 |

|Probability P(X) |0.4 |0.17 |0.2 |0.13 |0.1 |

7. A lottery offers one $1000 prize, one $500 prize, and five $100 prizes. One thousand tickets are sold at $3 each. Find the expectation if a person buys one ticket. (8 pts)

8. A survey found that 21% of Americans watch fire woks on television of July 4. Find the variance of the number of individuals who watch fireworks on the television on July 4 if a random sample of 1000 Americans is selected. (5 pts)

9. Find the probabilities using the standard normal distribution P(z>2.83). (5 pts)

10. Find the z value that corresponds to the given area. (5 pts)

[pic]

11. The mean weight of loads of rock is 46.0 tons with a standard deviation of 8.0 tons. If 25 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 44.24 tons. Assume that the variable is normally distributed. (8 pts)

12. The average daily jail population in the US is 618,319. If the distribution is normal and the standard deviation is 50,200, find the probability that on a randomly selected day, the jail is between 500,000 and 600,000. (10 pts)

13. A television station estimates that 50% of college students watch the Super Bowl. For a sample of 120 students selected at random, what is the mean and variance of the number of students who watch this game? (10 pts)

14. Find the probability P(–0.62 < z < –0.01) using the standard normal distribution.

(5 pts)

15. If X is a normal random variable with standard deviation 2.00, and if the probability that X is less than 4.76 is .648 (as shown below), then what is the mean of X? (Note: the diagram is not necessarily to scale.) (5 pts)

[pic]

16. If a baseball player's batting average is 0.340 or 34%, find the probability that the player will have a bad season and only score at most 60 hits in 200 times at bat?

(5 pts)

17. The standard deviation of a distribution is 20. If a sample of 225 is selected, what is the standard error of the mean? (5 pts)

Test 4A

1. Using Table G, find the values for [pic] and [pic] for [pic] = .05 and n = 15. (5 pts)

2. A sample of the reading scores of 35 fifth-graders has a mean of 82. The standard deviation of the sample is 15. Find the 90% confidence interval of the mean reading scores of all fifth-graders. (8 pts)

3. A survey found that out of 200 workers, 168 said they were interrupted three or more times an hour by phone messages, faxes, etc. Find the 95% confidence interval of the population proportion of workers who are interrupted three or more times an hour. (8 pts)

4. A service station advertises that customers will have to wait no more than 30 minutes for an oil change. A sample of 28 oil changes has a standard deviation of 5.2 minutes. Find the 99% confidence interval of the population standard deviation of the time spent waiting for an oil change. (8 pts)

5. In a sample of 855 bartenders, 48% heard complaints from patrons about work. If the margin of error was 4.4%, what was the confidence level that was used? . (8 pts)

6. The winning team's scores in 7 high school basketball games were recorded. If the sample mean is 10.3 points and the sample standard deviation is 0.10 points, find the 90% confidence interval of the true mean. (8 pts)

7. What is the 95% confidence interval for the variance of exam scores for 28 algebra students, if the standard deviation of their last exam was 12.7? (8 pts)

8. A researcher conducted a study of the access speed of 45 hard drives and concluded that his maximum error of estimate was 28. If he were to conduct a second study to reduce the maximum error of estimate to 7, about how many hard drives should he include in his new sample? (8 pts)

9. Using the z table find the critical value (or values), where α = 0.01

(Right – tailed test) (5 pts)

10. Find the critical value (or values) for the t test for each.

n =10 α = 0.05 Right – tailed (5 pts)

11.

|25 |32 |35 |25 |30 |26.5 |26 |25.5 |29.5 |32 |

|30 |28.5 |30 |32 |28 |31.5 |29 |29.5 |30 |34 |

|29 |32 |27 |28 |33 |28 |27 |32 |29 |29.5 |

The average one-year-old (both sexes) is 29 inches tall. A random sample of 30 one-year-olds in a large day care franchise resulted in the following heights. At ( = 0.05, can it be concluded that the average height differs from 29 inches? (Hint find H0 & H1) (8 pts)

Mean = 29.45 s = 2.61

12. Is the statement [pic]: = 6 a valid null hypothesis? (8 pts)

13. It has been reported that 40% of the adult population participates in computer hobbies during their leisure time. A random sample of 180 adults found that 65 engaged in computer hobbies. At ( = 0.01, is there sufficient evidence to conclude that the proportion differs from 40%? (Hint find H0 & H1) (8 pts)

14. If the observed value is 8, the expected value is 5, and the standard error is 2, then the test value used for the z test is equal to what? (5 pts)

15. Reginald Brown, an inspector from the Department of Weights and Measures, weighs 15 eighteen-ounce cereal boxes of corn flakes. He finds their mean weight to be 17.78 ounces with a standard deviation of 0.4 ounces. Are the cereal boxes lighter than they should be? Let [pic] . (8 pts)

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