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Question 1 Does a pandemic affect attitudes toward taxation? A series of studies investigated this question

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Question 1

Does a pandemic affect attitudes toward taxation? A series of studies investigated this question. Subjects (100 of them) were split at random into two groups. The control group read daily sports articles. The other group read daily articles about the pandemic. Afterwards, participants responded to a questionnaire about future rates of acceptable taxation. We are interested in views concerning acceptable taxation rates. Which of the following would have been the best method to display the two data sets?

0 Two side-by-side boxplots

0 A pie chart

0 A scatterplot

0 Two dot plots

0 A histogram

0 A contingency table

0 A bar plot

0 None of the above are appropriate

 

Question 2

Consider a random variable X with a Normal (2, 15) distribution, a random variable Y with a Normal (-6, 4) distribution and Cov X, Y) = 1. What is the distribution of W = X-2Y+3?

0 Normal (17.29)

0 Normal (17.21)

0 Normal (17.5)

0 Normal (17.31)

0 Normal (17.32)

0 Normal (17.24)

0 Normal (17.8)

0 Normal (17.34)

 

Question 3

Three cards are drawn at random from a pack of cards where the aces were removed. Calculate the probability that exactly two cards are of one denomination? Which interval does the probability belong?

0 (0.00.0.05)

0 (0.05.0.10)

0 (0.10.0.15)

0 (0.15.0.20)

0 (0.20.0.25)

0 (0.25. 0.30)

0 (0.30. 0.35)

0 none of the above intervals

Question 4

We are interested in whether panic attacks depend on the days of the week. Consider the results of a longitudinal study where the numbers of panic attacks were recorded in BC over a given time period.

Day of attack	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Number Recorded	15350	13819	13258	13033	12426	13863	16838

 

Which graphical method would best display the above data?

0 Two side-by-side boxplots

0 A pie chart

0 A scatterplot

0 Two dot plots

0 A histogram

0 A contingency table

0 A bar plot

0 None of the above are appropriate

Question 5

If we complete a P-value using a once –sided H₁, but now want to change to a two-sided H₁, how would the p-value change?

0 A. p-value would stay the same.

0 B. p-value would be multiplied by 0.5

0 C. p-value would decrease by a multiple less than 0.5

0 D. p-value would be multiplied by 2.0

0 E. p-value would increase by a multiple less than 0.5

0 F. p-value would increase by a positive additive constant

0 G. p-value would decrease by positive additive constant

0 H. None of above.

Question 6

Suppose that the number of cars going by your house in a one-minute interval is Poisson (3.2). It takes you 5 seconds to cross the street and you wait for a car to pass before you cross the street. Calculate the probability that you cross the street safely. The probability lies in the interval:

0 (0.0.0.1)

0 (0.10.2)

0 (0.2.0.3)

0 (0.3.0.4)

0 (0.4.0.5)

0 (0.5.0.6)

0 (0.6.0.7)

0 (0.7.1.0)

Question 7

Two engineering schools were surveyed. The first random sample of 250 engineers had 80 women, and the second random sample of 175 engineers had 40 women. The approximate 80% confidence interval for the different in proportions of women in these two engineering school is:

0 (0.025, 0.157)

0 (0.024, 0.158)

0 (0.023, 0.159)

0 (0.022, 0.160)

0 (0.021, 0.161)

0 (0.020, 0.162)

0 not possible- the underlying distribution is not normal

0 None of A-F

Question 8

A doctor states that 70% of his patients have high cholesterol levels. With patients arriving to his office randomly, what is the probability that the doctor must see more than five patients until at least three of them have high cholestoral levels. The probability lies in the interval:

0 (0.00, 0.05)

0 (005, 0.10)

0 (0.10, 0.15)

0 (015,020)

0 (0.20,0.25)

0 (0.25.0.30)

0 (0.30, 0.35)

0 none of the above intervals.

 

Question 9

Ina particular game, two fair dice are tossed. If the total number of spots showing is a six, you win $6, if the number of spots showing is a five, you win $3, and if the number of spots showing is 11, you win $2. Otherwise, you win nothing. Let X be the money you win. The standard deviation of X falls in which of the intervals:

0 (00.0.5)

0 (0.5.1.0)

0 (1.0.1.5)

0 (1.5.2.0)

0 (2.0.2.5)

0 (2.5.3.0)

0 (3.0.3.5)

0 none of the above.

Question 10

From a random sample of n students, we obtain the symmetric 95% confidence interval (0.62, 0.68) for the proportion of students who believe that the pandemic has negatively impacted their education. The corresponding 90% confidence interval is:

0 (0.610, 0.690)

0 (0.625, 0.675)

0 (0.605, 0.690)

 0 (0.630, 0.670)

 0 (0.635, 0.665)

 0 (0.640, 0.660)

0 impossible to determine

0 possible to determine but none of A-F

Question 11

This is not a realistic problem. The pmf of a random variable X is given by Prob(X=2) = 0.1+ θ, Prob(X=5) = 0.3-2θ. Prob(X=8) = 0.4+ θ. Prob(X=10) = 0.2 where -0.10 < θ < 0.15. In a test of HO: θ =-0.1, the null hypothesis is rejected if X=2 or if X=10. What is the significance level of the test?

(0.0, 0.125)

(0.125, 0.250)  

(0.250, 0.375)

(0.375, 0.500)

(0.500, 0.625)

(0.625, 0.750)

(0.750, 0.875)

(0.875, 1.000)

Question 12

Consider the random variable X with cumulative distribution function F(x) = 2x for 0 < x < 0.2 and

F(x) = 0.4+ (x-0.2) for 0.2 x < 0.8. The mean of X falls in which of these intervals:

(0.05, 0.10)

(0.10, 0.15)

(0.15, 0.20)

(0.20, 0.25)

(0.25, 0.30)

(0.30, 035)

(0.35, 0.40)

none of the above

Question 13

A groundskeeper paces out a soccer pitch with paces which can be taken to be independent from some distribution with mean 0.99 m and standard deviation 0.11 m. The groundskeeper takes one hundred such paces to mark out the pitch.

Estimate the probability that the total of the 100 paces is less than 100 m. The probability lies in the interval:

0 (0.000, 0.125)

0 (0.125, 0.250)

0 (0.250.0.375)

0 (0.375, 0.500)

0 (0.500, 0.625)

0 (0.625, 0.750)

0 (0.750, 0.875)

0 (0.875, 1.000)

Question 14

Randomly select 2 cells with replacement from the picture below:

1				2
3	4		5	6
7	8	9	10	11
12	13	14	15	16
17	18	19	20	21

 

Obtain the probability that two selected cells are in the same column.

0 1/7

0 1/6

0 1/4

0 2/5

0 1/5

0 2/21

0 1/21

0 none of the above

Question 15

In baseball, a player with a batting average of 300 suggests that over the next 20 at-bats, the number of hits X that he obtains has a Binomial (20, 0.3) distribution. This assumption is likely incorrect. Choose the statement which best explains the short comings of the distributional assumption.

0 The player's value p=0.3 is not likely correct

0 The trials (i.e. at-bats) are not independent

0 X is a continuous random variable

0 X is not Binomial because it is not a success/failure random variable

0 The trials (i.e. at-bats) do not have a common p

0 the parameter n=20 is random

0 two of the statements above are correct

0 three of the statements above are correct

Question 16

Customer arrive at a bank and the time that it takes them to be served is exponentially distributed with mean 6.0 minutes. For the next 10 customers that enter the bank, calculate the probability that exactly four of them will be served in less than 5.0 minutes. The probability lies in the interval:

(0.000, 0.125)

(0.125, 0.250)

(0.250, 0.375)

(0.375, 0.500)

(0.500, 0.625)

(0.625, 0.750)

(0.750, 0.875)

(0.875, 1.000)

 

Question 17

A researcher is interested in whether union workers earned significantly higher wages than non-union workers last year. She interviewed 12 union workers and 15 non-union workers, and their wages are shown below:

	Sample size	Sample Mean	Sample SD
Union	12	16.21	1.36
Non-Union	15	12.94	1.69

 

Test the null hypothesis of no difference between the wages of union workers and non-union workers.

Let X = wages earned of union workers, and Y = wages earned of non-union workers.

Let µ_X = the population mean wage of union workers, and µ _y = the population mean wage of non-union workers.

State the alternative hypothesis.

A. H₀: X^- = ?

B. Ho: X^- > ?

C. H₀: X^- ≥ ?

D. H₀: X^- < ?

E. H₀: X^- ≤ ?

F. H₀: X^+? = 0

G. H₀: X^- - ? = 0

H. none of the above

0 A

0 B

0 C

0 D

0 E

0 F

0 G

0 H

Question 18

It is assumed that plants given fertilizer die with probability 0.2 and that plants that are not given fertilizer die with probability 0.3. If 45 randomly chosen plants are given fertilizer and 55 randomly chosen plants are not given fertilizer, approximate the probability that at least 70 plants will survive. The probability lies in the interval:

0 (0.000, 0.125)

0 (0.125, 0.250)

0 (0.250, 0.375)

0 (0.375, 0.500)

0 (0.500, 0.625)

0 (0.625, 0.750)

0 (0.750, 0.875)

0 (0.875, 1.000)

Question 19

Some researchers have suggested that blood pressure may tend to be higher on average when measured on a subject's right arm than on their left arm. A doctor decided to investigate this conjecture by taking readings of the systolic blood pressure on both arms of a random selection of twelve patients at his practice. Suppose the data gathered. in mm Hg. are as given below:

Patient	1	2	3	4	5	6	7	8	9	10	11	12
Left arm blood pressure	161	166.8	164.6	160.1	156.9	147.3	152.6	173.7	153.8	164.8	170.7	162.9
Right arm BP	151	141.2	162.3	154.4	164.2	175.5	164.9	148.5	149.6	168.2	160.2	161

 

The coefficient of variation is estimated as cv1 s/x where s is the sample standard deviation and xbar is the sample mean. You might also consider estimating the coefficient of variation by cv2 = s/xmed where xmed is the sample median. Calculate T = cv1. - cv2 corresponding to left arm blood pressure. Which of the following is true:

0 T lies in the interval (0.0000. 0.0001)

0 T lies in the interval (0.0001. 0.0002)

0 T lies in the interval (0.0002. 0.0003)

0 T lies in the interval (0.0003. 0.0004)

0 T lies in the interval (0.0004. 0.0005)

0 T lies in the interval (0.0005. 0.0006)

T lies in the interval (0.0006. 0.0007)

0 T does not lie within any of the above intervals

Question 20

The proportion of new small businesses that go out of business in under three years in a city is believed to follow the distribution with density function

 f(x) = θ (θ +1) x θ-1 (1-x)

for 0 <x< 1, where θ> 0 is an unknown parameter. Which of the following is the value of E(X2)?

0 θ /( θ +2)

0 θ

0 θ (θ +1)

0 1.0

0 θ^2

0 θ(θ+1)/(( θ+2)( θ+3))

0 θ (θ +1)

0 none of the above