Câu 1 (Choose 1 answer - Multiple Choice)
Which of the following is a discrete quantitative (numerical) variable?
A. The Dow Jones Industrial average
B. The volume of water released from a dam
C. The distance you drove yesterday
D. The number of employees of an insurance company
Câu 2 (Choose 1 answer - Multiple Choice)
A summary measure that is computed to describe a characteristic of an entire population is called
A. an ordered array
B. a summary table
C. a statistic
D. a parameter
Câu 3 (Choose 1 answer - Multiple Choice)
The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a Blu-ray player made by the company over the past 12 months are satisfied with their products. The manager decides to ask a sample of customers, who have bought a Blu-ray player made by the company and filed a complaint over the past year, to fill in a survey about whether they are satisfied with the product. This method will most likely suffer from
A. nonresponse error
B. measurement error
C. coverage error
D. non-probability sampling
Câu 4 (Choose 1 answer - Multiple Choice)
TRUE or FALSE: The question "Is your household income last year somewhere between $50,000 and $100,000?" will most likely result in coverage error.
A. True
B. False
Câu 5 (Choose 1 answer - Multiple Choice)
An insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance. A representative from a local insurance agency selected a random sample of insured drivers and recorded, X, the number of claims each made in the last 3 years, with the following results (X/f): 0/14; 1/18; 2/12; 3/5; 4/1.
How many total claims are represented in the sample?
A. 15
B. 50
C. 111
D. 250
Câu 6 (Choose 1 answer - Multiple Choice)
At a meeting of information systems officers for regional offices of a national company, a survey was taken to determine the number of employees the officers supervise in the operation of their departments, where X is the number of employees overseen by each information systems officer. (X/frequency): 1/7; 2/5; 3/11; 4/8; 5/9.
How many regional offices are represented in the survey results?
A. 5
B. 11
C. 15
D. 40
Câu 7 (Choose 1 answer - Multiple Choice)
True or False: Given below is the scatter plot of the price/earnings ratio versus earnings per share of 20 U.S. companies. There appears to be a negative relationship between price/earnings ratio and earnings per share.
A. True
B. False
Câu 8 (Choose 1 answer - Multiple Choice)
True or False: Given below is the scatter plot of the market value (thousands$) and profit (thousands$) of 50 U.S. companies. There appears to be a negative relationship between market value and profit.
A. True
B. False
Câu 9 (Choose 1 answer - Multiple Choice)
True or False: The Guidelines for Developing Visualizations recommend always including a scale for each axis if the chart contains axes.
A. True
B. False
Câu 10 (Choose 1 answer - Multiple Choice)
A student's exam score average is a weighted mean of five exam scores. Find the student's exam score average, where the weighted mean is computed according to the following table (Exam/Score/Weight): 1/70/10%; 2/65/20%; 3/80/25%; 4/83/25%; 5/89/20%.
A. 69.65
B. 71.20
C. 76.50
D. 78.55
Câu 11 (Choose 1 answer - Multiple Choice)
True or False: As a rule, a value is considered an extreme value if its Z score is greater than -3.
A. True
B. False
Câu 12 (Choose 1 answer - Multiple Choice)
Suppose the mean math SAT score is 530, with a standard deviation of 110. Compute the Z-score for a test score of 650.
A. 1.09
B. 1.3
C. -1.09
D. -1.3
Câu 13 (Choose 1 answer - Multiple Choice)
Determine the first quartile $Q_{1}$ of the following data: 4, 6, 12, 14, 15, 15, 23, 25, 25, 32, 35, 41, 45, 51, 55.
A. 14
B. 15
C. 25
D. 12
Câu 14 (Choose 1 answer - Multiple Choice)
Calculate the population standard deviation: 6, 6, 10, 15, 17, 20, 20.
A. 5.65
B. 5.24
C. 5.38
D. 6.12
E. 6.45
Câu 15 (Choose 1 answer - Multiple Choice)
Suppose you have a dataset consisting of two variables, X and Y. If the units of measurement for both X and Y are changed (e.g., from meters to centimeters for X and from kilograms to grams for Y), which of the following statements about the coefficient of correlation between X and Y is true?
A. The coefficient of correlation will change in the same proportion as the change in units of measurement.
B. The coefficient of correlation will be halved.
C. The coefficient of correlation will be doubled.
D. The coefficient of correlation will remain the same.
E. The change in the coefficient of correlation cannot be determined based on the change in units of measurement alone.
Câu 16 (Choose 1 answer - Multiple Choice)
If two events are 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
Câu 17 (Choose 1 answer - Multiple Choice)
The probability that the new car needs a warranty repair is 0.05, the probability that the car is manufactured by a U.S-based company is 0.70, and the probability that the new car needs a warranty repair and was manufactured by a US-based company is 0.02. Are need for a warranty repair and location of the company manufacturing the car independent?
A. Yes, they are.
B. No, they are not.
C. Not enough information to give an answer.
Câu 18 (Choose 1 answer - Multiple Choice)
If $P(A)=0.3$, $P(B|A)=0.8$ and $P(B|A^{\prime})=0.5$, calculate $P(A|B)$.
A. 0.407
B. 0.590
C. 0.350
D. 0.240
Câu 19 (Choose 1 answer - Multiple Choice)
Seven passengers are on a waiting list for an overbooked flight. As a result of cancellations, 3 seats become available. How many ways can those 3 available seats be filled regardless of the order?
A. 35
B. 50
C. 40
D. 45
Câu 20 (Choose 1 answer - Multiple Choice)
The following table contains the probability distribution for X = the number of traffic accidents reported in a day. Find the probability of at least two accidents. (P(X): 0/0.10, 1/0.20, 2/0.45, 3/0.15, 4/0.05, 5/0.05).
A. 0.25
B. 0.70
C. 0.30
D. 0.75
E. None of the other choices is correct
Câu 21 (Choose 1 answer - Multiple Choice)
A die is rolled 26 times and let X be the number of twos that come up. Find the standard deviation of X.
A. 4.33
B. 3.61
C. 1.90
D. 2.08
Câu 22 (Choose 1 answer - Multiple Choice)
The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year. Find the probability that there will be exactly 3 power outages in a year.
A. 0.0892
B. 0.1512
C. 0.5000
D. 0.3158
E. None of the other choices is correct
Câu 23 (Choose 1 answer - Multiple Choice)
Given the following probability distributions for random variables X and Y: (P(x,y)/X/Y): 0.2/-100/50; 0.4/50/30; 0.2/200/20; 0.2/300/20. Compute E(X+Y).
A. 100
B. 30
C. 130
D. 77.14
E. None
Câu 24 (Choose 1 answer - Multiple Choice)
The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a randomly selected bottle will be less than 32 oz? (Given $P(Z < -0.25) = 0.4013$).
A. 0.3821
B. 0.0987
C. 0.5987
D. 0.4013
E. None of the other choices is correct
Câu 25 (Choose 1 answer - Multiple Choice)
The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected teacher earns more than $525 a week?
A. 0.2177
B. 0.1003
C. 0.7823
D. 0.2823
E. None of the other choices is correct
Câu 26 (Choose 1 answer - Multiple Choice)
Suppose the time interval between two consecutive defective light bulbs from a production line has a uniform distribution over an interval from 0 to 90 minutes. What is the probability that the time interval between two consecutive defective light bulbs will be at least 80 minutes?
A. 0.11
B. 0.89
C. 0.23
D. 0.77
Câu 27 (Choose 1 answer - Multiple Choice)
The average student spends about 17 hours each week preparing for classes ($SD = 5$ hours). If you select a random sample of 20 students, there is a 90% chance that the sample mean is less than how many hours per week?
A. 17
B. 19.54
C. 16.28
D. 18.44
E. None of the other choices is correct
Câu 28 (Choose 1 answer - Multiple Choice)
According to a survey, only 15% of customers visited the web site made a purchase. Random samples of size 50 are selected. The standard deviation of all the sample proportions is:
A. 0.05050
B. 0.08552
C. 0.4045
D. 0.2572
E. None of the other choices is correct
Câu 29 (Choose 1 answer - Multiple Choice)
A sample of weights: 150, 147, 136, 180, 173, 117, 168, 170. What is the width of 95% confidence interval estimate for the mean weight? ($\sigma = 16.7$, normal distribution).
A. 23.15
B. 11.57
C. 13.96
D. 27.93
E. None of the other choices is correct
Câu 30 (Choose 1 answer - Multiple Choice)
A study involves 634 deaths, 32 caused by accidents. Construct a 98% confidence interval for the true percentage of all deaths caused by accidents.
A. 3.61% < π < 6.48%
B. 3.34% < π < 6.75%
C. 3.02% < π < 7.07%
D. 2.80% < π < 7.29%
E. None of the other choices is correct
Câu 31 (Choose 1 answer - Multiple Choice)
If you want to be 95% confident of estimating the population proportion to within a sampling error of ±0.01 and the population proportion is approximately 0.40, what sample size is needed?
A. 9220
B. 6456
C. 97
D. 81
Câu 32 (Choose 1 answer - Multiple Choice)
Carter Motor Company claims its sedan will average better than 23 mpg. Identify the type I error for the test.
A. Rejecting the claim that it's more than 23 when it really is more than 23.
B. Failing to reject the claim that it's at most 23 when it is actually greater than 23.
C. Rejecting the claim that it's at most 23 when it really is at most 23.
Câu 33 (Choose 1 answer - Multiple Choice)
Find the test statistic to test the claim that the population mean is $31^\circ C$, given $n=40, \bar{x}=32, s=5$.
A. 1.26
B. 1.96
C. 1.99
D. 1.57
E. None of the other choice is correct
Câu 34 (Choose 1 answer - Multiple Choice)
Test $\mu > 132$ at $\alpha = 0.05$ with $n=40, \bar{x}=143.2, s=14.2$. Compute the test statistic and critical values.
A. -2.23 and 1.685
B. 2.23 and 1.685
C. -0.06 and 2.023
D. 0.06 and 2.023
Câu 35 (Choose 1 answer - Multiple Choice)
Test $H_0: \pi \le 0.35$ vs $H_1: \pi > 0.35$. Calculate the test statistic for: 40 out of 80 subjects have the characteristic.
A. 2.81
B. 1.88
C. -0.94
D. -1.87
E. None of the other choices is correct
Câu 36 (Choose 1 answer - Multiple Choice)
Comparing American vs Japanese managers' motivation scores. Which test would likely be most appropriate?
A. Paired t test
B. Pooled-variance t test for the difference between two means
C. F test for the ratio of two variances
D. Z test for the difference between two proportions
Câu 37 (Choose 1 answer - Multiple Choice)
Find the test statistic to test the claim $\mu_1 < \mu_2$. ($n_1=25, \bar{x}_1=15, s_1=1.5; n_2=20, \bar{x}_2=18, s_2=1.6$).
A. -4.18
B. -6.47
C. -6.43
D. -8.02
Câu 38 (Choose 1 answer - Multiple Choice)
True or False: In the paired t-test for the mean difference, the sample sizes must be equal in the two groups.
A. True
B. False
Câu 39 (Choose 1 answer - Multiple Choice)
In testing for differences between the means of two related populations, the null hypothesis is:
A. (i) $H_0: \mu_D = 1$
B. (ii) $H_0: \mu_D > 0$
C. (iii) $H_0: \mu_D < 0$
D. (iv) $H_0: \mu_D = 0$
Câu 40 (Choose 1 answer - Multiple Choice)
Comparing the percentage of claims between two moving companies (Econo-Move vs On-the-Move). Which test would be used?
A. t test for the difference between two means
B. F test for the ratio of variances
C. Separate variance t test for the difference between two means
D. Z test for the difference between two proportions
Câu 41 (Choose 1 answer - Multiple Choice)
What assumptions are necessary for testing evidence of a difference in variabilities? (i) Normal distribution; (ii) Random and independent samples.
A. Only (i)
B. Only (ii)
C. Neither (i) nor (ii)
D. Both (i) and (ii)
Câu 42 (Choose 1 answer - Multiple Choice)
In a one-way ANOVA, if the computed F statistic is greater than the critical F value you may:
A. (i) reject $H_0$ since there is evidence all the means differ.
B. (ii) reject $H_0$ since there is evidence that not all the means are equal.
C. (iii) not reject $H_0$ since there is no evidence of a difference in the means.
D. (iv) not reject $H_0$ because a mistake has been made.
Câu 43 (Choose 1 answer - Multiple Choice)
In a two-way ANOVA, the degrees of freedom for the interaction term is:
A. $(r-1)(c-1)$
B. $rc(n-1)$
C. $(r-1)$
D. $rcn+1$
Câu 44 (Choose 1 answer - Multiple Choice)
The error sum of squares (SSE) of the regression output provided is:
A. 0.1117
B. 3.1282
C. 25.9438
D. 29.0720
Câu 45 (Choose 1 answer - Multiple Choice)
Regression model: $\hat{Y}_i = 2.05X_i + 1.23$. What is the interpretation of the Y-intercept coefficient?
A. Predicted mean score is 1.23 when student does not study.
B. For each hour increase, change in mean score is +2.05.
C. For each hour increase, change in mean score is +1.23.
D. Predicted mean score is 2.05 when student does not study.
Câu 46 (Choose 1 answer - Multiple Choice)
What is the ratio SSR/SST called?
A. The coefficient of correlation
B. The coefficient of determination
C. The coefficient of variation
D. The adjusted coefficient of determination
Câu 47 (Choose 1 answer - Multiple Choice)
Which of the following is NOT one of the four assumptions of linear regression?
A. Linearity
B. Independence of errors
C. Normality of errors
D. Non-equal variance
Câu 48 (Choose 1 answer - Multiple Choice)
Regression $\hat{y} = 3.94 - 2.14x$, $n=5$, standard error of slope = 1.5. Find the test statistic for a positive linear relationship.
A. -1.43
B. 1.43
C. 2.63
D. -2.63
E. None of the other choices is correct
Câu 49 (Choose 1 answer - Multiple Choice)
Multiple regression for sales ($Y$) based on Capital ($X_1$) and Wages ($X_2$). Intercept = 15800, Capital Coeff = 0.1245, Wages Coeff = 7.0762. Predicted sales for $500M capital and $200M wages?
A. 15,800.00
B. 16,520.07
C. 17,277.49
D. 20,455.98
Câu 50 (Choose 1 answer - Multiple Choice)
From the ANOVA table provided (Total SS = 5922.17, Regression SS = 2593.13, $n=100$), determine the mean square error (MSE).
A. 26.73
B. 27.30
C. 30.45
D. 33.57
E. None of the other choices is correct
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