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QUESTIONS BANK (STAT 110)
Use the following to answer questions (1-9):
Suppose that you have the following set of numbers: 8, 2, 5, 3, 6, 7, 4, 5.
1. The value of the mean is ……..
(A) 5 (B) 4.25 (C) 4 (D) 6.
2. The value of the mode is ……..
(A) 2 (B) 5 (C) 4 (D) 3
3. The value of the first quartile (Q 1 ) is ……..
(A) 2.5 (B) 3.5 (C) 2 (D) 3.
4. The value of the interquartile range (IQR) is ……...
(A) 3.15 (B) 4 (C) 3 (D) 3.
5. The value of the variance is ……..
(A) 5.5 (B) 5 (C) 4.5 (D) 4
6. The value of the midrange is ……..
(A) 4 (B) 5.5 (C) 5 (D) 4.
7. The value of the coefficient of variation is ……..
(A) 55.4 % (B) 55 % (C) 40 % (D) 50 %
8. From the values of the mean, median, and mode, you can conclude that the
distribution of these data is ……..
(A) positively skewed. (C) negatively skewed.
(B) symmetric. (D) left-skewed.
9. The distribution of these data is called …….. distribution.
(A) bimodal (B) trimodal (C) unimodal (D) multimodal
10. If we have measured the weights of a sample of 50 persons and computed their
median, this will be an example of …….. statistics.
(A) descriptive (B) inferential (C) predictive (D) population
11. Nationality is an example of what level of measurement?
(A) ordinal (B) nominal (C) ratio (D) interval
Use the following frequency distribution to answer questions (12-17).
Class Limits 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 Total
Frequency 3 4 6 5 2 20
12. The number of classes is ……..
(A) 3 (B) 6 (C) 4 (D) 5
13. What is the width of the class 60 -70?
(A) 15 (B) 10 (C) 20 (D) 5
14. The modal class is ……..
(A) 70 - 80 (B) 60 - 70 (C) 50 - 60 (D) 40 - 50
15. The value of the range is ……..
(A) 50 (B) 45 (C) 40 (D) 55
16. Using the class 70 - 80 , the lower class limit, and the class midpoint are
…… and ……, respectively.
(A) 69.5, 75 (B) 69.75, 70 (C) 80, 70 (D) 70, 75
17. What is the cumulative frequency for the class 70 - 80?
(A) 16 (B) 12 (C) 18 (D) 17
18. When data are categorized as Saudi, Egyptian, Syrian, and Sudanese, the most
appropriate measure of central tendency is the ………
(A) mean (B) median (C) midrange (D) mode
The following is a histogram for the statistics scores of a group of 50 students.
Use this histogram to answer questions (19-20).
19. The distribution of statistics scores is ……..
(A) positively skewed. (C) negatively skewed.
(B) right-skewed. (D) symmetric.
20. What do you expect for the values of the mean, median, and mode?
(A) mean = median (C) mean < median
(B) mean > median (D) mean = mode
21. If a student scored 80 points on a test where the mean was 75 and the student's
z-score was 0.5, then the standard deviation, s, must be ……..
(A) 10 (B) 12 (C) 8 (D) 15
- Determine the type of relationship shown in the figure below.
(A) there is no relationship (B) positive (C) negative (D) curvelinear
- The correlation coefficient between the amount of fats لدةون كمية which a person eats and his or her weight may be:
(A) close to -1 (B) close to 2 (C) close to 1 (D) 0
- An emergency service center wishes to see whether a relationship between the
outside temperature ( x ) and the number of emergency calls (y) exists. The data are shown here: n = 5 ∑ x = 9 ∑ y = 17 ∑ xy = 28 ∑ x^2 = 23 ∑y^2 = 71 Compute the value of the correlation coefficient.
(A) -0.274 (B) 0.247 (C) 0.274 (D) -0.
The equation of the regression line between a person's age in years ( x ) and the number of hours he exercises per week (y) is given by: y' = 25 – 0.4 x. Use the above equation to answer the questions (36-37).
- The correct statement that represents the relationship between ( x ) and (y) is:
(A) When the number of hours he exercises increases by 1 hour, his age increases
by 0.4 years.
(B) When the number of hours he exercises decreases by 1 hour, his age
decreases by 25 on average.
(C) When a person's age increases by 1 year, the number of hours he
exercises decreases by 0.4 on average.
(D) When a persons's age Increases by 1 year, the number of hours he
exercises increases by 0.4 on average.
- Predict the number of hours a person exercises per week when his age is 50 years.
(A) 4 (B) 5 (C) 3 (D) 1.
In the study of the relationship between the number of absences ( x ) and the final
grade (y) of 6 students in the statistics class, the data are shown as follows.
∑ x = 42 , ∑ y = 470 , ∑ x y = 3143 , ∑ x^2 = 354 , ∑y^2 = 37358
Answer the following two questions (38 -39)
- The slope of the regression line is ………
(A) 3.45 (B) -2.45 (C) -3.45 (D) 2.
- The value of the correlation coefficient is …….
(A) -0.82 (B) 1 (C) 0.92 (D) 0.
- If the correlation coefficient (r) equals 0.6, then the relationship can be described as ……..
(A) weak and linear. (B) moderate and nonlinear.
(C) positive, strong and nonlinear. (D) positive, moderate and linear.
- As x increase, y decrease and vice versa. Then, the relationship between the two
variables, x and y, can be described as:
(A) positive relationship (B) negative relationship
(C) no relationship (D) (A) and (B)
- What is the range of values for the correlation coefficient?
(A) -1 to 2 (B) -1 to 1 (C) -2 to 1 (D) -2 to 2
- If the value of the correlation coefficient equals 0.9, then the type of the relationship is:
(A) strong negative (C) weak positive
(B) strong positive (D) moderate negative
A fair die is rolled once.
Answer questions (44-46).
44. What is the probability of getting a 4?
(A) 5/6 (B) 2/6 (C) 1/6 (D) 6/
- What is the probability of getting an even number?
(A) 1/6 (B) 3/6 (C) 4/6 (D) 2/
- What is the probability of getting a number greater than 3?
(A) 1/2 (B) 1 (C) 2/3 (D) 1/
- Two fair dice are rolled. What is the probability of getting a sum of 3?
(A) 5/18 (B) 2/9 (C) 5/36 (D) 1/
Let X denote the number of accidents that occur in a city during a week. The following table lists the probability distribution of X.
Number of accidents 3 4 5 6 Probability P( x ) 0. 2 0. 3 0. 3 0. 2
Use the probability distribution given above to answer questions (58-59).
- The mean of the distribution is ……..
(A) 3.5 (B) 4.5 (C) 2.5 (D) 3
- The variance of the distribution is ……..
(A) 1.05 (B) 0.89 (C) 0.85 (D) 1.
- A survey found that 2 out of 5 students say that they like statistics course. If 3 students are selected at random, find the probability that exactly one student would have liked the statistics course.
(A) 0.525 (B) 0.455 (C) 0.432 (D) 0.
- If 20% of T.V.s are defective معيبة , the mean and standard deviation of the number of defective T.V.s for a sample of 100 T.V.s are …….. and …….., respectively.
(A) 20 and 4 (B) 25 and 4 (C) 20 and 16 (D) 25 and 16
- If a player rolls one die and gets 6 , he wins $120. The cost to play the game is $15. What is the expected value of his gain?
(A) $6 (B) $8 (C) $5 (D) $
- If a player draws a card from an ordinary deck and gets 10 , he wins $104. If he gets a picture, he looses $26. What is the expected value of his gain?
(A) $4 (B) $2 (C) $6 (D) $
- How many different 2-digit numbers can be formed from the digits in the number 235?
(A) 4 (B) 5 (C) 6 (D) 3
- How many different tests can be made from a test bank of 5 questions if the test consists of 4 questions?
(A) 4 (B) 6 (C) 3 (D) 5
Use the following to answer Questions (66-70): The probability that Student A will pass the statistics exam is 0.8, and the probability that student B will pass the same exam is 0.6. Find the following probabilities:
- Both students (A and B) will pass the exam.
(A) 0.16 (B) 0.72 (C) 0.80 (D) 0.
- Only one of them will pass the exam.
(A) 0.35 (B) 0.44 (C) 0.36 (D) 0.
- Student A will pass the exam and Student B will fail the exam.
(A) 0.27 (B) 0.07 (C) 0.63 (D) 0.
- At least one of them will pass the exam.
(A) 0.95 (B) 0.85 (C) 0.92 (D) 0.
- Both students (A and B) will fail the exam.
(A) 0.08 (B) 0.50 (C) 0.52 (D) 0.
- If X is a discrete random variable with ∑ [x^2 P(x)] = 30 and E(x) = 5. The variance of the probability distribution of X is ……..
(A) 2 (B) 1.5 (C) 3 (D) 5
Two dice, A and B, are rolled. Let X represents the sum of the two numbers of spots that will appear. Answer questions (72-74).
- What is the probability of X = 5 is?
(A) 4/36 (B) 1/12 (C) 3/18 (D) 5/
- Find the probability: P( A = 2│X = 3).
(A) 3/4 (B) 1/2 (C) 5/18 (D) 1/
- Find the probability: P(B = 3).
(A) 1/6 (B) 5/6 (C) 7/36 (D) 1/
- A coin is rolled three times, the probability of getting two tails is ……..
(A) 1/2 (B) 3/4 (C) 5/8 (D) 3/
- A die is rolled three times, the probability of getting a 3 twice is ……..
(A) 5/72 (B) 1/24 (C) 5/36 (D) 1/
- The outcomes of each trial in a binomial experiment ……..
(A) must be fixed (B) are dependent (C) are unlimited (D) are independent
- Which of the following is a binomial experiment?
(A) Asking 5 people if they are smokers.
(B) Rolling a die to see the number of spots appear on the die.
(C) Drawing two balls without replacement from a box contains 2 white balls, 5
red balls, and 3 black balls.
(D) Asking 50 people which brand of cigarettes they smoke.
- P( 65 < X < 80 )
(A) 0.2857 (B) 0.7143 (C) 0.2975 (D) 0.
- P(X = 60)
(A) 0 (B) 0.25 (C) 1 (D) 0.
The time T 1 to travel from A to B through city centre (road R 1 ) is normally distributed with a mean of 20 minutes and a standard deviation of 5 minutes. The time T 2 to travel from A to B through a new ring road (road R 2 ) is normally distributed with a mean of 15 minutes and a standard deviation of 8 minutes. You have 17 minutes to travel from A to B on an important appointment. Using this information, solve questions (92 to 94).
- P(T 1 > 17)
(A) 0.2743 (B) 0.2347 (C) 0.4723 (D) 0.
- P(T 2 > 17)
(A) 0.0031 (B) 0.0013 (C) 0.4013 (D) 0.
- Your correct decision is …….
(A) R 1 is better than R 2. (B) Both R 1 and R 2 are the same.
(C) R 2 is better than R 1. (D) Insufficient information to make a decision.
- The total area under the standard normal curve is ……..
(A) 0 (B) 1 (C) 0.5 (D) 2
- Approximately what percentage of normally distributed data values will fall within 2 standard deviation above or below the mean?
(A) 95% (B) 68% (C) 99.7% (D) 99%
- The standard normal distribution is ……..
(A) skewed to the right. (B) skewed to the left.
(C) symmetric. (D) asymmetric.
The time (X) needed to complete a final examination in a particular college course is normally distributed with a mean of 60 minutes and a standard deviation of 10 minutes.
Answer questions (98 to 100).
- What is the probability of completing the exam in less than 70 minutes?
(A) 0.1587 (B) 0.9655 (C) 0.8413 (D) 0.
- What is the probability that a student will complete the exam in more than 75
minutes but less than 80 minutes?
(A) 0.9965 (B) 0.0404 (C) 0.9956 (D) 0.
- The best point estimate of the population mean is the …….
(A) sample mean. (B) sample median.
(C) sample mode. (D) sample midrange.
A research firm conducted a survey to determine the mean amount smokers spend on cigarettes during a day. A sample of 100 smokers revealed that the sample mean is $5 and sample standard deviation is $ 2. Assume that the sample was drawn from a normal population.
Answer questions (101-104).
- The point estimate of the population mean is ……..
(A) 2 (B) 5 (C) 6 (D) 100
- The lower limit of the 95% confidence interval for the population mean is ……..
(A) 4.5 (B) 5.5 (C) 4.6 (D) 5.
- The upper limit of the 95% confidence interval for the population mean is ……..
(A) 5.2 (B) 5.5 (C) 6.2 (D) 5.
- The width of the 95% confidence interval for the population mean is ……
(A) 0.8 (B) 1 (C) 1.2 (D) 0.
- The maximum error of estimate is ……..
(A) 0.6 (B) 0.4 (C) 0.5 (D) 0.
- When a 99% confidence interval is calculated instead of a 95% confidence interval with n being the same. The maximum error of estimate will be …….
(A) smaller. (B) larger. (C) the same. (D) It cannot be determined.
If one wishes to test the claim that the mean of the population is 50.
Answer questions (107-108).
- The appropriate null hypothesis is ……..
(A) μ ≠ 50 (B) μ ≥ 50 (C) μ ≤ 50 (D) μ = 50
- The appropriate alternative hypothesis is ……..
(A) μ ≠ 50 (B) μ ≥ 50 (C) μ ≤ 50 (D) μ = 50
A researcher wishes to test the claim that the average productivity of items
produced per hour by a machine is 50 units per hour. This machine was observed
for 64 hours, and the average productivity of items produced per hour and the
standard deviation were found to be 53 and 10 , respectively.
To test the validity of this claim, and using α = 0.05 , Answer questions (109-112).
- The null and alternative hypotheses are ……..
(A) (B) (C) (D)
H 0 : μ = 50 H 0 : μ = 52 H 0 : μ = 52 H 0 : μ = 50 H 1 : μ ≠ 52 H 1 : μ ≠ 50 H 1 : μ ≠ 50 H 1 : μ ≠ 50
