AnswersAZ-Common Core Algebra II BStatistical Inferences

Statistical Inferences Answers

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1
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A simple random sample of 60 is drawn from a normally distributed population, and the mean is found to be 28, with a standard deviation of 5. Which of the following values is within the 95% confidence interval (z-score = 1.96) for the population mean?Remember, the margin of error, ME, can be determined using the formula .

Question illustration
A
The value of 26, because it’s not greater than 26.7 and less than 29.3.
B
The value of 27, because it’s greater than 26.7 and less than 29.3.
C
The value of 32, because it’s greater than 23 and less than 33.
D
The value of 34, because it’s not greater than 23 and less than 33.
2
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What is the z-score with a confidence level of 95% when finding the margin of error for the mean of a normally distributed population from a sample?

A
0.99
B
1.65
C
1.96
D
2.58
3

A simple random sample of 85 is drawn from a normally distributed population, and the mean is found to be 146, with a standard deviation of 34. Which of the following values is outside the 99% confidence interval for the population mean? Use the table below to help you answer the question.Confidence Level90%95%99%z*-score1.6451.962.58Remember, the margin of error, ME, can be determined using the formula .

Question illustration
A
the value of 135 because it is not greater than 136.5
B
the value of 137 because it is greater than 136.5
C
the value of 138 because it is less than 153.2
D
the value of 154 because it is greater than 153.2
4

A simple random sample of 90 is drawn from a normally distributed population, and the mean is found to be 138, with a standard deviation of 34. What is the 90% confidence interval for the population mean? Use the table below to help you answer the question.Confidence Level90%95%99%z*-score1.6451.962.58Remember, the margin of error, ME, can be determined using the formula .

Question illustration
A
128.75 to 147.25
B
130.98 to 145.02
C
132.10 to 143.90
D
137.38 to 138.62
5

Which of the following conditions must be met in order to make a statistical inference about a population based on a sample if the sample does not come from a normally distributed population?

A
Mu greater-than-or-equal-to 30
Option A
B
x Overbar greater-than-or-equal-to 30
Option B
C
n greater-than-or-equal-to 30
Option C
D
Upper N greater-than-or-equal-to 30
Option D
6

All else being equal, if you cut the sample size in half, how does this affect the margin of error when using the sample to make a statistical inference about the mean of the normally distributed population from which it was drawn?.

Question illustration
A
The margin of error is multiplied by .
Option A
B
The margin of error is multiplied by .
Option B
C
The margin of error is multiplied by 0.5.
D
The margin of error is multiplied by 2.
7

Which of the following z-values, standard deviations, and sample sizes produce a margin of error of 0.95?

Question illustration
A
z = 2.14; s = 4; n = 9
B
z = 2.14; s = 4; n = 81
C
z = 2.14; s = 16; n = 9
D
z = 2.14; s = 16; n = 81
8

A simple random sample is drawn from a normally distributed population, and when making a statistical inference about the population mean, the margin of error is found to be 5.9 at a 95% level of confidence. If the mean of the sample is 18.7, what is the 95% confidence interval for the population mean?

A
18.7 ± 5.9
B
18.7 ± 9.7
C
18.7 ± 11.6
D
18.7 ± 15.2
9

Dawn and Pablo are members of a normally distributed population that is being sampled. If the chance of Dawn being included in the sample is 0.05%, what must the chance of Pablo being included in the sample be in order to be able to make inferences about the population based on the sample?

A
0%
B
greater than 0% and less than 0.05%
C
0.05%
D
greater than 0.05%
10

The times it took for 35 loggerhead sea turtle eggs to hatch in a simple random sample are normally distributed, with a mean of 50 days and a standard deviation of 2 days. Assuming a 95% confidence level (95% confidence level = z-score of 1.96), what is the margin of error for the population mean?Remember, the margin of error, ME, can be determined using the formula .

Question illustration
A
0.06
B
0.11
C
0.34
D
0.66
11

Which of the following statements is correct?

A
Population parameters are used to make inferences about sample statistics.
B
Population statistics are used to make inferences about sample parameters.
C
Sample parameters are used to make inferences about population statistics.
D
Sample statistics are used to make inferences about population parameters.
12

Which of the following conditions must be met in order to make a statistical inference about a population based on a sample if the sample does not come from a normally distributed population?

A
Mu greater-than-or-equal-to 30
Option A
B
x Overbar greater-than-or-equal-to 30
Option B
C
n greater-than-or-equal-to 30
Option C
D
Upper N greater-than-or-equal-to 30
Option D
13

The number of sit-ups that all tenth-grade girls can do in 5 minutes is normally distributed. Beth surveyed 20 of her fellow intramural tennis players, all tenth-grade girls, and determined the mean number of sit-ups they could do. Can she make an inference about the population mean for all tenth-grade girls based on the sample?

A
No, because the sample size was not big enough.
B
No, because she did not use a simple random sample.
C
Yes, because the sample size was big enough.
D
Yes, because she used a simple random sample.
14

A random sample shows that 48% of students prefer learning programming through games, with a margin of error of ±4% at 95% confidence.

A
Exactly 48% of all students prefer game-based learning.
B
Between 44% and 52% of all students prefer game-based learning.
C
95% of students prefer game-based learning.
D
At least 52% of students prefer game-based learning.
15

A simple random sample of 85 is drawn from a normally distributed population, and the mean is found to be 146, with a standard deviation of 34. Which of the following values is outside the 99% confidence interval for the population mean? Use the table below to help you answer the question.Confidence Level90%95%99%z*-score1.6451.962.58Remember, the margin of error, ME, can be determined using the formula .

Question illustration
A
the value of 135 because it is not greater than 136.5
B
the value of 137 because it is greater than 136.5
C
the value of 138 because it is less than 153.2
D
the value of 154 because it is greater than 153.2
16

Which of the following z-values, standard deviations, and sample sizes produce a margin of error of 0.95?

Question illustration
A
z = 2.14; s = 4; n = 9
B
z = 2.14; s = 4; n = 81
C
z = 2.14; s = 16; n = 9
D
z = 2.14; s = 16; n = 81
17

The times it took for 35 loggerhead sea turtle eggs to hatch in a simple random sample are normally distributed, with a mean of 50 days and a standard deviation of 2 days. Assuming a 95% confidence level (95% confidence level = z-score of 1.96), what is the margin of error for the population mean?Remember, the margin of error, ME, can be determined using the formula .

Question illustration
A
0.06
B
0.11
C
0.34
D
0.66
18

Suppose the mean of a normally distributed population is 300, and 200 simple random samples are drawn from the population. At a 68% confidence level, (one standard deviation from the mean), about how many of the samples’ confidence intervals would you expect to contain the population mean?

A
64
B
96
C
136
D
204
19

A simple random sample is drawn from a normally distributed population. The value of which of the following will not be known for certain but can be inferred?

A
Mu
Option A
B
x Overbar
Option B
C
s
D
n
20

What is the z-score with a confidence level of 95% when finding the margin of error for the mean of a normally distributed population from a sample?

A
0.99
B
1.65
C
1.96
D
2.58

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