AnswersMathematics III AHypothesis Testing

Hypothesis Testing — Unit test Answers

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According to a poll, 56% of voters support funding a new community center. A surveyor randomly selects 75 voters and asks each voter if he or she is in favor of the center. If being in favor of the center is a success, what is the probability of a success for this binomial experiment?

A
0.34
B
0.44
C
0.56
D
0.75
2
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You pick a card at random from an ordinary deck of 52 cards. If the card is a diamond, you get some points; if not, you lose 2 points. What value for the diamonds would make the game fair?

A
12
B
6
C
24
D
3
3

The stem-and-leaf plot below shows the number of pages each student in a class read the previous evening.Which statement is true about the data set?

Question illustration
A
Its median is greater than its mode.
B
It has a range of 52 pages.
C
The value of the first quartile is 13.
D
The data is symmetric.
4

The graph below is used by company 2 to show the average monthly electric cost based on the electricity provider.How could the graph be redrawn so that the difference in monthly electric cost does not appear as great?

Question illustration
A
The scale on the y-axis could be changed to 0–150.
B
The scale on the y-axis could be changed to 100–120.
C
The interval on the y-axis could be changed to count by 1s.
D
The interval on the y-axis could be changed to count by 20s.
5

Sonia rolls a six-sided number cube 12 times and records if she rolls a 2. What is the number of trials for this binomial experiment?

A
2
B
6
C
12
D
18
6

Black Marble Points

S
Since E(black) = 0.24 and E(red) = 0.16, Seth should choose to play black marbles.
E
E(red) will be twice that of E(black), so Seth should choose to play red marbles.
S
Since E(red) = E(black), it is a fair game, so it doesn’t matter which color Seth chooses.
B
Both options will lose points because there are two ways to lose points and only one way to gain points. He should choose neither color.
7

To conduct a survey about the type of phone service most people in Greenville prefer, 10 different blocks in the neighborhood are chosen. On these 10 blocks, 10 houses are selected at random, and then each resident of each of those houses is interviewed. This type of sampling method is

A
simple random sampling.
B
stratified sampling.
C
systematic random sampling.
D
cluster sampling.
8

A simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is , while the standard deviation is s. What is the 99% confidence interval for the population mean? Use the table below to help you answer the question.Confidence Level90%95%99%z*-score1.6451.962.58

Question illustration
A
x Overbar plus-or-minus StartFraction 0.90 times s Over StartRoot n EndRoot EndFraction
Option A
B
x Overbar plus-or-minus StartFraction 0.99 times s Over StartRoot n EndRoot EndFraction
Option B
C
x Overbar plus-or-minus StartFraction 1.645 times s Over StartRoot n EndRoot EndFraction
Option C
D
x Overbar plus-or-minus StartFraction 2.58 times s Over StartRoot n EndRoot EndFraction
Option D
9

The annual salaries of all employees at a financial company are normally distributed with a mean = $34,000 and a standard deviation = $4,000. What is the z-score of a company employee who makes an annual salary of $28,000?

Question illustration
A
–5
B
–3.5
C
–1.5
D
1.5
10

The difference between an observational study and an experiment is that

A
in an observational study, only one group is studied, and in an experiment, two groups are studied.
B
in an observational study, the researchers do not control treatment, and in an experiment, they do.
C
in an experiment, cause-and-effect is analyzed, and in an observational study, it is not.
D
in an experiment, one group is studied over a short period of time, and in an observational study, the group is studied over a longer period of time.
11

A local weather enthusiast wants to see if the last five summers have been warmer than normal for Eloy, Arizona. From the National Oceanic and Atmospheric Administration (NOAA), he knows the 30-year average for July was 90° with a standard deviation of 2.1°. The last five summers recorded have an average of 93.5°. If he uses a = 5%, which of the following would be valid based on the data he has gathered?

A
He can conclude that the summers have been warmer than the 30-year average.
B
He can conclude that the summers will continue to be warmer for the next 10 years.
C
He does not have enough information to make a decision.
D
The average for the last five years fits with the 30-year average.
12

When finding the margin of error for the mean of a normally distributed population from a sample, what is the critical probability, assuming a confidence level of 58%?

A
0.21
B
0.42
C
0.58
D
0.79
13

Which of the following is a valid probability distribution?

A
Probability distribution A is shown. The probabilities of 1, 2, 3, 4, 5 and 6 are all 0.2.
Option A
B
Probability distribution B is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.3; 4 is 0.3; 5 is 0.2; 6 is 0.1.
Option B
C
Probability distribution C is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.4; 5 is 0.1; 6 is 0.1.
Option C
D
Probability distribution D is shown. The probability of 1 is 0.2; 2 is 0.1; 3 is 0.1; 4 is 0.5; 5 is 0.1.
Option D
14

Sonia rolls a six-sided number cube 12 times and records if she rolls a 2. What is the number of trials for this binomial experiment?

A
2
B
6
C
12
D
18
15

Stan guessed on all 10 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that he got at least 2 questions correct? Round the answer to the nearest thousandth.

Question illustration
A
0.211
B
0.244
C
0.756
D
0.944
16

In Juneau, Alaska, the 30-year annual snowfall average is 86.7 inches with a standard deviation of 40.4 inches. The last four years saw an average annual snowfall of 115.7 inches, 62.9 inches, 168.5 inches, and 135.7 inches. Hia performs a hypothesis test on this data to determine if the next 30-year norm will have a different average if the trend from the last four years continues. She uses a significance level of 5%. Which of the following is a conclusion that she may make?

A
The z-statistic is 1.44, so the null hypothesis cannot be rejected.
B
The z-statistic is 1.68, so the null hypothesis cannot be rejected.
C
The z-statistic is 1.85, so the null hypothesis should be rejected.
D
The z-statistic is 4.6, so the null hypothesis should be rejected.
17

The table below shows the ages of houses to the nearest year in a neighborhood. Using the age of the houses as the random variable, X, which graph shows the probability distribution, PX(x), of a randomly chosen house?Age of HouseNumber of Houses115220325430

A
A probability distribution is shown. The probability of 1 is 0.16; 2 is 0.22; 3 is 0.28; 4 is 0.33.
Option A
B
A probability distribution is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.3; 4 is 0.4.
Option B
C
A probability distribution is shown. The probability of 1 is 0.65; 2 is 0.1; 3 is 0.12; 4 is 0.13.
Option C
D
A probability distribution is shown. The probability of 1 is 0.15; 2 is 0.2; 3 is 0.25; 4 is 0.3.
Option D
18

Destiny performs a hypothesis test on a population with µ = 115 and . Her sample size is 25 with a mean of 120.4. Which of the following correctly depicts the z-statistic for this data?

Question illustration
A
0.04
B
0.90
C
3.53
D
3.93
19

According to a poll, 56% of voters support funding a new community center. A surveyor randomly selects 75 voters and asks each voter if he or she is in favor of the center. If being in favor of the center is a success, what is the probability of a success for this binomial experiment?

A
0.34
B
0.44
C
0.56
D
0.75
20

The scores of the students on a standardized test are normally distributed, with a mean of 500 and a standard deviation of 110. What is the probability that a randomly selected student has a score between 350 and 550? Use the portion of the standard normal table below to help answer the question.zProbability0.000.50000.250.59870.350.63680.450.67361.000.84131.260.89611.350.91151.360.9131

A
9%
B
24%
C
59%
D
91%

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