Statistics Exam 1

For two events A and B, suppose P(A) = 0.6, P(B) = 0.2, and P(A|B) = 0.7, then P(A U B) =

0.66

Fifty percent of all technical assistants would like to have a PC. Eighty percent of all technical assistants would like to have MAC. Fourty-five percent of all technical assistants would like to have both. If a technical assistant is randomly selected, what is the probability that she would like to have a PC or a MAC?

0.85 or 85%

Relationship between median, mean, and distribution shape 1) skewed left (negatively skewed) 2) symmetric 3) skewed right (positively skewed)

1) mean < median 2) mean = median 3) mean > median

A recent survey found that 24% of people in Michigan like oatmeal. If the probability that someone lives in Michigan is 4.8%, what is the probability that someone lives in Michigan and likes oatmeal?

1.2%

A city police officer using radar checked the speed of 26 cars as they were travelling down a city street and the data is given as below:27 23 22 38 43 24 25 23 22 54 31 30 29 48 27 25 29 28 26 33 25 21 23 34 20 23What are the mean, median and mode for this dataset?

29, 26.5, 23

A sample was taken of the salaries of four employees from a large company. The following are their salaries (in thousands of dollars) for this year: 33, 36, 41, and 47. The variance of their salaries is approximately

37.58

A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes) required to make this trip was 38, 33, 36, 47, and 41. What is the standard deviation for these sample data?

5.34

The mean life of a particular brand of light bulb is 1200 hours. If you know that at about 95% of this brand of bulbs will last between 1100 and 1300 hours, then what is the standard deviation of the light bulbs' life?

50

The heights of four fifth grade students are 58, 56, 60 and 62 inches. What are the mean, median and standard deviation of this dataset, and the standard deviation of the new dataset by adding 2 to each number, i.e., 60, 58, 62, 64?

58, 58, 2.58, 2.58

A data set contains the following six values. 13, 24, 17, 32, 29, 24 a. Find the population standard deviation. b. Find the population variance.

6.517 ; 42.472

Jessica Salas, President of Salas Products, is reviewing the warranty policy for her company's new model of automobile batteries. Life tests performed on a sample of 100 batteries indicated: (1) an average life of 75 months, (2) a standard deviation of 5 months, and (3) a bell-shaped battery life distribution. Approximately 95% of the batteries will last between

65 and 85 months

A statistics student made the following grades on 7 tests: 76, 82, 92, 95, 79, 86, and 92. What is the mean grade?

86

A statistics student made the following grades on 7 tests: 76, 82, 92, 95, 79, 86, and 92. What is the median grade?

86

Researchers often wish to know the color preference of consumers and might ask consumers to specify their favorite color, such as red, blue, yellow or purple. This is an example of what level of data?

Nominal

Members of the accounting department's clerical staff were asked to rate their supervisor's leadership style as either (1) authoritarian or (2) participatory. This is an example of

Nominal level data

One investigating company tracked all credit card purchase during 2012 and measured two variables: (1) the type of credit card used (VISA, MasterCard, American Express, or Discover), and (2) the amount (in dollars) of each purchase. Identify the level of each variable measured.

Nominal level, Ratio level

A study was conducted to investigate the effect of a coal-fired generating plant upon the water quality of a river. As part of an environmental impact study, fish were captured, tagged, and released. The following information was recorded for each fish: sex (0 = female, 1 = male), length (cm), maturation (0 = young, 1 = adult), weight (g). The level of these data is:

Nominal, ratio, ordinal, ratio

Researchers often wish to measure consumers' satisfaction toward certain products and might ask consumers to specify their feelings as either "very dissatisfied," "somewhat dissatisfied," "somewhat satisfied," or "very satisfied." This is an example of what level of data?

Ordinal

What is the level of data corresponding to a military rank (Lieutenant, Captain, Major)?

Ordinal

Morningstar Mutual Funds analyzes the risk and performance of mutual funds. Each mutual fund is assigned an overall rating of one to five stars. One star is the lowest rating, and five stars is the highest rating. This level of measurement is

Ordinal level

You are the owner of a camping site and want to estimate the average age of your customers. For this purpose, you select a representative sample of your clients and offer them a discount on their next visit as compensation for filling out a short questionnaire that includes relevant age intervals: "Your age is (a) 30 or younger, (b) 30 to 40, (c) 40 to 50, (c) 50 to 60, (d) 60 or older." This is an example of

Ordinal level

If two events, Event A with probability P(A) and Event B with probability P(B) are mutually exclusive, then

P (A ∩ B) = 0

Which level of data measurement allows the most or broadest application of statistical techniques?

Ratio

Which of the following statements captures a key aspect of ratio level data?

Ratio data have an absolute zero, the zero value represents the absence of the characteristic being studied

A large manufacturing company in Indianapolis produces valves for the chemical industry. According to specifications, one particular valve is supposed to have a five-inch opening on the side. Quality control inspectors take random samples of these valves just after the hole is bored. They measure the size of the hole in an effort to determine if the machine needs to be adjusted. The measurement of the diameter of the hole represents which level of data?

Ratio level

The Magnolia Swimming Pool Company wants to determine the average number of years it takes before a major repair is required on one of the pools that the company constructs. The president of the company asks Rick Johnson, a company accountant, to randomly contact fifty families that built Magnolia pools in the past ten years and determine how long it was in each case until a major repair. The information will then be used to estimate the average number of years until a major repair for all pools sold by Magnolia. The average based on the data gathered from the fifty families can best be described as a

Statistic

If stock A has a coefficient of variation of 30% and stock B has a coefficient of variation of 35%. Based on this measure of risk, which stock would be considered riskier?

Stock B

Which of the following operations is meaningful for processing nominal data?

Counting

Which of the following statements in not true? a) The union probability is the probability of X or Y occurring b) The conditional probability uses subtotal of the possible outcomes in denominator. c) The marginal probability uses the total possible outcomes in the denominator d) The joint probability uses the probability of X in the denominator.

D) The joint probability uses the probability of X in the denominator

Which of the following statements about population parameters is most appropriate?

Inferences about population parameters are always subject to uncertainty

A cancer research group was interested in determining the percentage of women 40 years or older that have regularly scheduled mammograms. To accomplish this, they surveyed 500 women in this age group and based on the 155 women that responded affirmatively, estimated the percentage of all women in this age group that have regularly scheduled mammograms. This process is an example of

Inferential statistics

A new sales person is paid a commission on each sale. This person made $2,000 in commission his first month on the job. From this he concludes that he will make $24,000 during his first year. This is an example of

Inferential statistics

A student makes an 82 on the first test in a statistics course. From this, she estimates that her average at the end of the semester (after other tests) will be about 82. This is an example of

Inferential statistics

On discovering an improperly adjusted drill press, Jack Joyner, Director of Quality Control, ordered an inspection of every fifth casting drilled during the evening shift. Less than 1% of the sampled castings were defective; so, Jack released the evening shift's production to assembly. This is an example of

Inferential statistics

A business is attempting to find the best small town in the United States in which to relocate. As part of the investigation, the elevations of all small towns in the United States are researched. Some towns are located high in the Rockies with elevations over 8,000 feet. There are even some towns located in the south central valley of California with elevations below sea level. These elevations can best be described as which level of data?

Interval level

Which scale of measurement has these two properties: linear distance is meaningful and the location of origin (or zero point) is arbitrary?

Interval level

If it were not for the existence of an "absolute zero," ratio data would be considered the same as

Interval level data

You are the owner of a camping site and want to evaluate the feasibility of opening earlier during the year. For this analysis, you obtain the average maximum and minimum local daily temperatures for early spring. This is an example of

Interval level data

Parametric statistics require that data be

Interval or ratio

Which types of data are normally called metric data?

Interval or ratio level data

A distribution of numbers is approximately bell shaped. If the mean of the numbers is 129 and the standard deviation is 11, a. between what two numbers would approximately 68% of the values fall? b. Between what two numbers would 95% of the values fall? c. Between what two values would 99.7% of the values fall?

a. between 118 and 140 b. between 107 and 151 c. between 96 and 162

The states of 'heads' or 'tails' on a coin can be defined as follows:

collectively exhaustive, complementary, and mutually exclusive

Compare the variability of the following two sets of data by using both the population standard deviation and the population coefficient of variation. Data Set 1: 49, 82, 77, 54 Data Set 2: 159, 121, 138, 152

population standard deviation: Data Set 1 = 14.21 Data Set 2 = 14.53 population coefficient of variation: Data Set 1 = 21.69% Data Set 2 = 10.19%

A city police officer using radar checked the speed of 26 cars as they were travelling down a city street and the data is given as below:27, 23, 22, 38, 43, 24, 25, 23, 22, 54, 31, 30, 29, 48, 27, 25, 29, 28, 26, 33, 25, 21, 23, 34, 20, 23 it is most like that the distribution of the dataset is

positively skewed

Which of the following statements is not true regarding probabilities

probabilities are subjective measures with limited value in business

The method of assigning probabilities based on the principle that the probability of an event occurring is equal to the number of times the event has occurred in the past divided by the total number of opportunities for the event to have occurred is the

relative frequency of occurrence method

The mean of a distribution is 13, the median is 15, and the mode is 18. It is most likely that this distribution is

skewed left

Belinda Bose is reviewing a newly proposed advertising campaign. Based on her 15-years' experience, she believes the campaign has a 75% chance of significantly increasing brand name recognition of the product. This is an example of assigning probabilities using the ________________ method.

subjective probability method

For a set of data with a distribution skewed to the left

the mean is lower than the median