STAT 125-HK Business Statistics Midterm Exam

STAT 125-HK Business Statistics Midterm Exam

Question 1

2 points

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The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that house sales will increase but interest rates will not during the next 6 months is:

a. 0.065
b. 0.15
c. 0.51
d. 0.89

Question 2

2 points

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The process of using sample statistics to draw conclusions about true population parameters is called

a. statistical inference.
b. the scientific method.
c. sampling.
d. descriptive statistics.

Question 3

2 points

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Which of the following is NOT a reason for obtaining data?

a. Data are needed to formulate a statistical model.
b. Data are needed to evaluate conformance to standards.
c. Data are needed to measure performance of an ongoing production process.
d. Data are needed to provide input to a study.

Question 4

2 points

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A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes. What proportion of customers having to hold more than 1.5 minutes will hang up before placing an order?

a. 0.86466
b. 0.60653
c. 0.39347
d. 0.13534

Question 5

2 points

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Selection of raffle tickets from a large bowl is an example of

a. sampling with replacement.
b. sampling without replacement.
c. subjective probability.
d. None of the above.

Question 6

2 points

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The width of each bar in a histogram corresponds to the

a. differences between the boundaries of the class.
b. number of observations in each class.
c. midpoint of each class.
d. percentage of observations in each class.

Question 7

2 points

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If two events are mutually exclusive and collectively exhaustive, what is the probability that one or the other occurs?

a. 0.
b. 0.50.
c. 1.00.
d. Cannot be determined from the information given.

Question 8

2 points

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Which of the following is not an element of descriptive statistical problems?

a. An inference made about the population based on the sample.
b. The population or sample of interest.
c. Tables, graphs, or numerical summary tools.
d. Identification of patterns in the data.

Question 9

2 points

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Which of the following statistics is not a measure of central tendency?

a. Mean.
b. Median.
c. Mode.
d. Q3.

Question 10

2 points

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Major league baseball salaries averaged $1.5 million with a standard deviation of $0.8 million in 1994. Suppose a sample of 100 major league players was taken. Find the approximate probability that the average salary of the 100 players exceeded $1 million.

a. Approximately 0
b. 0.2357
c. 0.7357
d. Approximately 1

Question 11

2 points

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If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs?

a. 0.
b. 0.50.
c. 1.00.
d. Cannot be determined from the information given.

Question 12

2 points

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TABLE 2-6

A sample of 200 students at a Big-Ten university was taken after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following table contains the result.
Did Well on Midterm

Did Poorly on Midterm

Studying for Exam

80

20

Went Bar Hopping

30

70

Referring to Table 2-6, of those who did well on the midterm in the sample, _______ percent of them went bar hopping the weekend before the midterm.

a. 15
b. 27.27
c. 30
d. 50

Question 13

2 points

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TABLE 2-5

The following are the durations in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier.

Time (in Minutes)

Relative Frequency

0 but less than 5

0.37

5 but less than 10

0.22

10 but less than 15

0.15

15 but less than 20

0.10

20 but less than 25

0.07

25 but less than 30

0.07

30 or more

0.02

Referring to Table 2-5, what is the width of each class?

a. 1 minute
b. 5 minutes
c. 2%
d. 100%

Question 14

2 points

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According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that annual household income is over $25,000 if the residents of a household do not own 2 cars is:

a. 0.12
b. 0.18
c. 0.40
d. 0.55

Question 15

2 points

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A study is under way in Yosemite National Forest to determine the adult height of American pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 60 feet tall. It is estimated that the forest contains 25,000 adult American pines. The study involves collecting heights from 250 randomly selected adult American pine trees and analyzing the results. Identify the population from which the study was sampled.

a. The 250 randomly selected adult American pine trees.
b. The 25,000 adult American pine trees in the forest.
c. All the adult American pine trees taller than 60 feet.
d. All American pine trees, of any age, in the forest.

Question 16

2 points

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When extreme values are present in a set of data, which of the following descriptive summary measures are most appropriate?

a. CV and range.
b. mean and standard deviation.
c. interquartile range and median.
d. variance and interquartile range.

Question 17

2 points

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A population frame for a survey contains a listing of 72,345 names. Using a table of random numbers, how many digits will the code numbers for each member of your population contain?

a. 3
b. 4
c. 5
d. 6

Question 18

2 points

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A recent survey of banks revealed the following distribution for the interest rate being charged on a home loan (based on a 30-year mortgage with a 10% down payment).

Interest Rate:

7.0%

7.5%

8.0%

8.5%

>8.5%

Probability

0.12

0.23

0.24

0.35

0.06

If a bank is selected at random from this distribution, what is the chance that the interest rate charged on a home loan will exceed 8.0%?

a. 0.06
b. 0.41
c. 0.59
d. 1.00

Question 19

2 points

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Referring to the histogram from Table 2-3, how many graduating seniors attended the luncheon?

a. 4
b. 152
c. 275
d. 388

Question 20

2 points

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TABLE 2-4

A survey was conducted to determine how people rated the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display of the data is shown below.

Stem

Leaves

3

24

4

03478999

5

0112345

6

12566

7

01

8
9

2

Referring to Table 2-4, what percentage of the respondents rated overall television quality with a rating between 50 and 75?

a. 0.11
b. 0.40
c. 0.44
d. 0.56

Question 21

2 points

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The Central Limit Theorem is important in statistics because

a. for a large n, it says the population is approximately normal.
b. for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size.
c. for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.
d. for any sized sample, it says the sampling distribution of the sample mean is approximately normal.

Question 22

2 points

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If you were constructing a 99% confidence interval of the population mean based on a sample of n = 25 where the standard deviation of the sample s = 0.05, the critical value of t will be

a. 2.7969
b. 2.7874
c. 2.4922
d. 2.4851

Question 23

2 points

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A statistics student found a reference in the campus library that contained the median family incomes for all 50 states. She would report her data as being collected using

a. a designed experiment.
b. observational data.
c. a random sample.
d. a published source.

Question 24

2 points

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TABLE 2-5

The following are the durations in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier.

Time (in Minutes)

Relative Frequency

0 but less than 5

0.37

5 but less than 10

0.22

10 but less than 15

0.15

15 but less than 20

0.10

20 but less than 25

0.07

25 but less than 30

0.07

30 or more

0.02

Referring to Table 2-5, if 10 calls lasted 30 minutes or more, how many calls lasted less than 5 minutes?

a. 10
b. 185
c. 295
d. 500

Question 25

2 points

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The employees of a company were surveyed on questions regarding their educational background and marital status. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is single or has a college degree is:

a. 0.10
b. 0.25
c. 0.667
d. 0.733