AnswersConcepts in Probability and Statistics - MA3120 B-CRUnit Test

Unit Test — Cumulative exam Answers

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1
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The table shows the height, in meters, of an object that is dropped as time passes until the object hits the ground.A line of best fit for the data is represented by h = –21.962x + 114.655. Which statement compares the line of best fit with the actual data given by the table?

Question illustration
A
According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.
B
According to the line of best fit, the object was dropped from a lower height.
C
The line of best fit correctly predicts that the object reaches a height of 40 meters after 3.5 seconds.
D
The line of best fit predicts a height of 4 meters greater than the actual height for any time given in the table.
2
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The frequency table shows a set of data collected by a doctor for adult patients who were diagnosed with a strain of influenza. Which dot plot could represent the same data as the frequency table?

Question illustration
A
A number line going from 25 to 45. There is 1 dot above 26, 28, 29, 33, 39, 44. There are 2 dots above 31, 35, 36, 38. There are 3 dots above 41.
Option A
B
A number line going from 25 to 45. There is 1 dot above 26, 28, 29, 33, 44. There are 2 dots above 30, 35, 38. There are 3 dots above 32, 40.
Option B
C
A number line going from 25 to 45. There is 1 dot above 26, 31, 33, 34, 41, 44. There are 2 dots above 30, 35, 37. There are 3 dots above 32, 40.
Option C
D
A number line going from 25 to 45. There is 1 dot above 26, 27, 33, 40, 44. There are 2 dots above 29, 30, 32, 35, 38, 45. There are 3 dots above 39.
Option D
3

Four sets of data have the trend lines shown below.Data Set 1Data Set 2Data Set 3Data Set 4Which trend line describes the set with the greatest rate of change?

Question illustration
A
y = 7.5 x + 3.8
Option A
B
y = 9.8 x + 6.7
Option B
C
y = 3.8 x + 7.5
Option C
D
y = 6.7 x + 9.8
Option D
4

The scatterplot below shows the number of hours that students read weekly and the number of hours that they spend on chores weekly.Which statement about the scatterplot is true?

Question illustration
A
As the number of hours of reading increases, the number of hours spent on chores decreases.
B
As the number of hours of reading increases, the number of hours spent on chores increases.
C
In general, the number of hours of reading does not affect the number of hours used for chores.
D
In general, the number of hours spent on chores is equal to the number of hours spent on reading.
5

The rates of change of two data sets can be compared by finding:

A
the initial values.
B
the slope of each trend line.
C
how close the points are to the line.
D
the y-intercepts.
6

The distribution of the values of a population is shown below, and a simple random sample is drawn from the population. Based on this information alone, can the sample be used to make inferences about the population?

Question illustration
A
No, because the population values appear to be normally distributed.
B
No, because the population values do not appear to be normally distributed.
C
Yes, because the population values appear to be normally distributed.
D
Yes, because the population values do not appear to be normally distributed.
7

The points (15, 10), (25, 20), (30, 22), (40, 32), (55, 53), (60, 55) represent the time, x, it takes 6 people to travel y miles. The scatterplot below represents the situation.TravelBased on the information above, how many miles should a person who drives for 48 minutes expect to travel?

Question illustration
A
32 miles
B
42 miles
C
48 miles
D
54 miles
8

The equation for the line of best fit is f(x) ≈ 1.8x − 5.4 for the set of values in the table.

Question illustration
A
14
B
20
C
45
D
54
9

Grace claims that the interquartile range of a data set is never equal to its range. Which type of set can be used to prove or disprove her claim?

A
A set consisting of identical elements will prove her claim.
B
A set consisting of different elements will prove her claim.
C
A set consisting of identical elements will disprove her claim.
D
A set consisting of different elements will disprove her claim.
10

The graph shows a distribution of data with a standard deviation of 6.

Question illustration
A
It is within 1 standard deviation of the mean.
B
It is within 2 standard deviations of the mean.
C
It is exactly 3 standard deviations from the mean.
D
It is exactly 4 standard deviations from the mean.
11

The histogram represents the daily low and high temperatures in a city during March. Which comparison of the distributions is true?

Question illustration
A
The distribution of low temperatures is nearly symmetric, and the distribution of high temperatures is nearly symmetric.
B
The distribution of low temperatures is skewed right, and the distribution of high temperatures is nearly symmetric.
C
The distribution of low temperatures is nearly symmetric, and the distribution of high temperatures is skewed right.
D
The distribution of low temperatures is skewed right, and the distribution of high temperatures is skewed right.
12

Weston completed a hypothesis test and found that he could not reject the null hypothesis. Which of the following is a valid reason for his conclusion?

A
The z-statistic is less than 0.
B
The z-statistic lies in the critical region.
C
The z-statistic is greater than 0.
D
The z-statistic lies outside the critical region.
13

The box plots show the average speeds, in miles per hour, for the race cars in two different races.Average Speeds of Cars in Race AAverage Speeds of Cars in Race BOne-half of cars travel at which speeds?

Question illustration
A
between 120 and 143 mph in race A; between 125 and 140 mph in race B
B
between 120 and 170 mph in race A; between 125 and 165 mph in race B
C
between 120 and 153 mph in race A; between 125 and 145 mph in race B
D
between 165 and 170 mph in race A; between 150 and 165 mph in race B
14

The graph below shows the amount of time Misha spent outside over a 30-day period. How might the graph be considered misleading?

Question illustration
A
The x-scale is different from the y-scale.
B
The x-interval makes the data appear skewed.
C
The y-scale is too large for the data set.
D
The y-interval shows exponential increase rather than linear increase.
15

Lisa and Jen are each reading a different 250-page book consisting of 10 chapters. Which statistics would be helpful in determining whose book shows the greater variability in the chapter length? Check all that apply.

A
the median of the chapter lengths in each book
B
the mean of the chapter lengths in each book
C
the interquartile range of the chapter lengths in each book
D
the range of chapter lengths in each book
16

The table shows the number of pages in the books in Box A and the number of pages in the books in Box B.Which statement is true about the data?

Question illustration
A
The mean of Box A is greater than the mean of Box B.
B
The mean of Box B is greater than the mean of Box A.
C
The median of Box A is greater than the median of Box B.
D
The median of Box B is greater than the median of Box A.
17

The box plots show the weights, in pounds, of the dogs in two different animal shelters.Weights of Dogs in Shelter AWeights of Dogs in Shelter BWhich describes the spread of the data in the two box plots?

Question illustration
A
The data in shelter A show more spread than the data in shelter B.
B
The data in shelter B show more spread than the data in shelter A.
C
The data in shelter A range from about 17 to 28, while the data in shelter B range from about 16 to 20.
D
The data in shelter A range from about 21 to 28, while the data in shelter B range from about 18 to 20.
18

Which measure of center is shown in a box plot?

A
mean
B
median
C
mode
D
range
19

The heights of the starting players on each of two basketball teams are shown in the table below.Heights of Starters on Team A and Team BTeam A70 in.72 in.75 in.68 in.70 in.Team B71 in.73 in.71 in.72 in.73 in.Jacob found that the mean height of Team A is 71 and the mean height of Team B is 72. He believes that because Team B has a greater mean, it also has a greater mean absolute deviation. Which explains Jacob’s error?

A
One of the means is incorrect, but the reasoning is correct.
B
Both of the means are incorrect, and the reasoning is also incorrect.
C
Both of the means are correct, but the reasoning is incorrect.
D
One of the means is incorrect, and the reasoning is also incorrect.
20

The table shows the probabilities of certain prizes in a restaurant’s contest where the first 100 customers are winners.

Question illustration
A
It increases the mean value of the prizes.
B
It decreases the mean value of the prizes.
C
It increases the median value of the prizes.
D
It decreases the median value of the prizes.

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