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Statistics 13B, Winter 2023, Practice Midterm I Version A

1. Which is a qualitative variable below?

(a) length of time between arrivals of buses at a terminal

(b) depth of sediments in a riverbed

(c)  score received in a homework out of 60 points

(d) time required to finish an exam

(e) manufacturers of cars parked in a parking lot

Answer: e

2. A market share of 78.5% would be represented in a pie chart by a slice with a central angle of

(a) 78.5 degrees

(b)  39.2 degrees

(c)  282.6 degrees

(d)  141.3 degrees

(e)  178.5 degrees

Answer: c (78.5 x (360/100) degrees)

3. The frequency table of the weights (in lbs.) of n trouts caught from a lake is given below.

Class (in lbs	Frequency	Relative Frequency
6.5 to less than 7.0 7.0 to less than 7.5 7.5 to less than 8.0 8.0 to less than 8.5 8.5 to less than 9.0 9.0 to less than 9.5	6 8 13 a 7 5	0.12 0.16 0.26 b 0.14 0.1

What is the value of n?

(a) 45        (b) 48        (c) 50        (d) 52        (e) 66

Answer: c

4. Refer to Problem 3. The histogram of the weights of trouts is

(a) bimodal

(b)  skewed left

(c) nearly symmetric

(d)  skewed right

(e) none of the above

Answer: c

5. For data sets with extreme values, which of the fol- lowing is the most appropriate measure of center

(a) mean

(b) range

(c) IQR

(d) median

(e)  standard deviation

Answer: d

6. If two data sets have the same range,

(a) the  distance  between  the  smallest  and  the largest observations in both sets will be the same

(b) the smallest and the largest observations are the same in both sets

(c) both sets have the same variance

(d) both sets have the same interquartile range

(e) if one set has an outlier, the other set has an outlier, too

Answer: a

7.  Suppose there are 10 measurements half of which take negative values and the other half take positive values. Then which of the following statements must be true about this data (choose the most appropriate one)?

(a) variance is zero

(b) range is negative

(c) mean is zero

(d)  standard deviation is nonnegative (e) both c and d

Answer: d

8. Below are the times recorded (in seconds) to com- plete a task for 10 subjects participating in a psycho- logical experiment:  100, 158, 160, 188, 200, 200, 205, 278, 290, 300. The mean is

(a) 100     (b) 150     (c) 207.9     (d) 290     (e) 300

Answer: c

9. If a data set with 201 observations has a mean of -2 and a standard deviation of 0.5, and an observation

with the value 1 is replaced by - 1, what is the new standard deviation?

(a) 0.4581     (b) 0.2100     (c) 0.4928     (d) 0.5050 (e) 0. 1050

Answer: a

10. The standard deviation of a data set is 4. If each mea- surement is multiplied by -2, the standard deviation of the resulting data set is

(a) 4          (b) 2          (c) 6          (d) 8          (e) -8

Answer: d

11. The number of raisins in 16 miniboxes of Sunmaid

was counted with the following results:  15, 19, 21, 21, 22, 23, 24, 25, 25, 27, 28, 28, 31, 32, 35 ,36 : the five-number summary is

(a)  21, 23, 25.5, 28.5, 35

(b)  15, 22, 25.5, 31.5, 36

(c)  15, 21.5, 25, 30.5, 36

(d)  19, 22.5, 25, 31.5, 42

(e)  15, 22, 25, 28, 36

Answer: c (Positions of Q1, Q2 and Q3 are 4.25, 8.5 and 12.75 in the ordered data)

12. Refer to Problem 11, how many outliers are there in this data set?

(a) 0          (b) 1          (c) 2          (d) 3          4 (e) 5

Answer: a (IQR=9; lower fence=7.75, upper fence=43.75)

13. There  are  519  student  enrolled  in  Stat  13.    As- sume the distribution of scores for the final exam is mounded-shaped with mean 70 and standard devia- tion 10. What is the approximate number of students

who scored 70 or less? (Round to nearest integer)    (a) 218      (b) 260      (c) 130      (d) 58      (e) 436

Answer: b

14. Refer to Problem 13, find the smallest interval, cen- tered at 70, that is guaranteed to contain approxi- mately 95 percent of the scores.

(a) (50, 90)         (b) (65, 85)         (c) (68.68, 81.32)

(d) (70.53, 79.47)                          (e) (71.84, 78. 16)

Answer: a

15. The distribution of the life time of electric bulbs is relatively mound-shaped (also a.k.a bell-shaped) with  mean  600  hours  and  standard  deviation  80 hours. Then the proportion of bulbs having life time between 520 and 680 hours is approximately

(a) 2 3/4   (b) < 1/2 (c) 0.99 (d) 0.95 (e) 0.68

Answer: e (Within 1 standard deviation of mean; ap- ply the Empirical rule)

16. A radio station claims that the amount of advertising each hour has a mean of 16 minutes and a sample variance of 1.9 minutes. You listen to the radio sta-

tion for 1 hour and observe that the amount of adver-

tising time is 14 minutes.  Calculate the z-score for this amount of advertising time.

(a) 1     (b) 1.05     (c) - 1.05     (d) - 1.45     (e) 2. 11

Answer: d