Read the questions carefully - FIRST determine if you are creating a confidence interval for a PROPORTION (use p-hat, the sample proportion) or a MEAN (use x-bar, a sample mean).
Keep in mind, you are using the statistic from a sample (p-hat or x-bar) to make inferences about a population (true proportion or true mean).
Read the questions carefully - FIRST determine if you are creating a confidence interval for a PROPORTION (use p-hat, the sample proportion) or a MEAN (use x-bar, a sample mean).
Keep in mind, you are using the statistic from a sample (p-hat or x-bar) to make inferences about a population (true proportion or true mean).
Question 1
1.
The scenario is:
In her first-grade social studies class, Jordan learned that 70% of Earth’s surface is covered in water. She wondered if this is true and asked her dad for help.
Do you think you will be working with a proportion or a mean?
Question 2
2.
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Question 3
3.
Question 4
4.
In her first-grade social studies class, Jordan learned that 70% of Earth’s surface is covered in water. She wondered if this is true and asked her dad for help.
To investigate, he tossed an inflatable globe to her 50 times, being careful to spin the globe each time. When Jordan caught it, her dad recorded where her right index finger was pointing. In 50 tosses, her finger was pointing to water 33 times.
For each answer round to two places past the decimal point
What is the margin of error for a 95% Confidence Interval? _______
What is the lower bound/limit for the 95% confidence interval? _______
What is the upper bound/limit for the 95% confidence interval? _______
Question 5
5.
Question 6
6.
The scenario is:
A particular reading test is scored from 0 to 500. A score of 243 is a “basic” reading level and a score of 281 is “proficient.”
Scores for a random sample of 1470 eighth-graders in Atlanta had the following results:
Do you think you will be working with a proportion or a mean?
Question 7
7.
Question 8
8.
A particular reading test is scored from 0 to 500. A score of 243 is a “basic” reading level and a score of 281 is “proficient.” Scores for a random sample of 1470 eighth-graders in Atlanta had the following:
Construct a 99% confidence interval for μ.
df = _______
t* = _______
For the following three answers: round to three places past the decimal.
What is the Margin of Error? _______
What is the Lower bound/limit of the 99% confidence interval? _______
What is the Upper bound/limit of the 99% confidence interval? _______
Question 9
9.
A particular reading test is scored from 0 to 500. A score of 245 is a “basic” reading level and a score of 281 is “proficient.”
Scores for a random sample of 1470 eighth-graders in Atlanta had the following:
Based on your 99% confidence interval, is there convincing evidence that the mean for all Atlanta eighth-graders is different than the basic level? Explain.
Question 10
10.
Question 11
11.
Our situation is:
What proportion of students are willing to report cheating by other students?
A student project put this question to an SRS of 172 undergraduates at a large university: “You witness two students cheating on a quiz. Do you go to the professor?”
Only 19 answered “Yes.”
Do you think you will be working with a proportion or a mean?
Question 12
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Question 13
13.
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An SRS of 172 undergraduates was conducted
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Question 14
14.
What proportion of students are willing to report cheating by other students?
A student project put this question to an SRS of 172 undergraduates at a large university: “You witness two students cheating on a quiz. Do you go to the professor?”
Only 19 answered “Yes.”
Create a 90% Confidence Interval:
What is z*? _______
For each answer round to three places past the decimal point
What is the margin of error? _______
What is the lower bound/limit for the 90% confidence interval? _______
What is the upper bound/limit for the 90% confidence interval? _______
Question 15
15.
Question 16
16.
What critical value t* from the t-Table should be used in constructing a confidence interval for the population mean in each of the following settings? Assume the conditions are met.
a. A 90% confidence interval based on n = 12 randomly selected observations _______
b. A 99% confidence interval based on a random sample of size 58 _______
c. A 95% confidence interval based on n = 85 randomly selected individuals _______
Question 17
17.
In Mr. Wright’s school district, students are allowed to take as much time as they need to finish the final exam in Algebra II. He asked a random sample of 45 of the 600 students who took the exam one year to record the length of time they spent on the exam.
The mean and standard deviation for the 45 students were:
Construct a 95% confidence interval for the mean completion time of all students who took the exam. Assume the conditions for inference are met.
Round answers to three places past the decimal.
degrees of freedom: df = _______
t* value: _______
Margin of Error = _______
Lower bound/limit of the 95% confidence interval = _______
Upper bound/limit of the 95% confidence interval = _______
Question 18
18.
because we are working with a percent (part of a whole) from a sample.
In her first-grade social studies class, Jordan learned that 70% of Earth’s surface is covered in water. She wondered if this is true and asked her dad for help.
To investigate, he tossed an inflatable globe to her 50 times, being careful to spin the globe each time. When Jordan caught it, her dad recorded where her right index finger was pointing. In 50 tosses, her finger was pointing to water 33 times.
What is the value for p-hat? (the sample proportion)
Match up the terms below.
1 sample t interval for mu
formula for calculating a proportion
p-hat
Sample statistic
1 sample z interval for p
Population parameter we are estimating
part/whole
p-hat value
p
not the p-hat value
0.33
Inference method we will use
0.66
Inference method we will not use
In her first-grade social studies class, Jordan learned that 70% of Earth’s surface is covered in water. She wondered if this is true and asked her dad for help.
To investigate, he tossed an inflatable globe to her 50 times, being careful to spin the globe each time. When Jordan caught it, her dad recorded where her right index finger was pointing.
In 50 tosses, her finger was pointing to water 33 times.
Are the conditions met for creating a 95% Confidence Interval?
Large Counts Condition was not met
Random Sample was not met
Random Sample was met by the SRS
Unable to be determined
Large Counts Condition was met by n(p-hat) > 10
Yes
Large Counts Condition was met by n(1-p-hat) > 10
No
Our class activity using random.org and random locations on a map found 71% of the earth is covered with water.
Do our results support Jordan's 95% confidence interval or do they give convincing evidence that her interval is incorrect?
because 71% is within the confidence interval.
because confidence intervals are complicated to calculate.
because 71% is not within the confidence interval.
Our results do not support Jordan's 95% confidence interval
This is difficult to determine
Our results support Jordan's 95% confidence interval
Proportion
because we are working with the average from a sample.
A particular reading test is scored from 0 to 500. A score of 243 is a “basic” reading level and a score of 281 is “proficient.”
Scores for a random sample of 1470 eighth-graders in Atlanta had the following:
Verify that the conditions are met for constructing a confidence interval for μ = true mean reading score for Atlanta eighth-graders.
Normal/Large Sample Condition is not met, the sample size is not > 30
Normal/Large Sample Condition is met: 42.17 > 30
Normal/Large Sample Condition is met: 1470 > 30
Random Sample Condition is not met: nothing shown in the description of the scenario above.
Normal/Large Sample Condition is met: 240 > 30
Random Sample Condition is met: 'random sample of 1470 eighth-graders'
No, there is not convincing evidence that the mean for all Atlanta eighth-graders is different than the basic level
because the basic level is above the confidence interval of plausible values.
because the basic level is below the confidence interval of plausible values.
Yes, there is convincing evidence that the mean for all Atlanta eighth-graders is different than the basic level
because the basic level is within the confidence interval of plausible values.
The athletic director at a large university records the resting heart rate for 65 randomly selected athletes. We use these data to construct a confidence interval for the mean resting heart rate for all athletes at this university.
Have the conditions been met for calculating a 95% confidence interval for the mean resting heart rate?
Normal/Large Sample condition was not met
No
Random Sample Condition was met
Normal/Large Sample condition: 65 is not greater than 30
Random Sample Condition: 65 athletes were randomly selected for the sample
Yes
Random Sample Condition was not met
Normal/Large Sample condition: n=65 > 30
Random Sample Condition: 65 athletes were selected
Normal/Large Sample condition was met
Proportion
because we are working with a percent (part of a whole) of a sample.
What proportion of students are willing to report cheating by other students?
A student project put this question to an SRS of 172 undergraduates at a large university: “You witness two students cheating on a quiz. Do you go to the professor?”
Only 19 answered “Yes.”
Match the following terms with the correct description:
1 sample t interval for mu
formula for calculating a proportion
1 sample z interval for p
Sample statistic
part/whole
Population parameter we are estimating
p-hat
p-hat value
0.19
not the p-hat value
0.11
Inference method we will use
p
Inference method we will not use
What proportion of students are willing to report cheating by other students?
A student project put this question to an SRS of 172 undergraduates at a large university: “You witness two students cheating on a quiz. Do you go to the professor?”
Only 19 answered “Yes.”
Are the conditions met for creating a 90% Confidence Interval?
Match the following information with the correct description:
Random Sample condition is met
153
Large Counts Condition is met for n*p-hat
172(0.11)
Large Counts Condition is met for n*(1- p-hat)
172(1-0.19)
value of n*p-hat
19
value of n*(1- p-hat)
172(1-0.11)
incorrect answer
The counselors from DHS conducted a survey of 186 Freshmen and Sophomores. They found that 24 students out of a random survey of 152 students would report cheating by other students at DHS.
Do our results support the 90% confidence interval or do they give convincing evidence that the students at DHS are more likely to report cheating by other students?
Our results support the 90% confidence interval
This is difficult to determine
because 15.8% is within the confidence interval of plausible values.
because 15.8% is not within the confidence interval of plausible values.
Our results do not support the 90% confidence interval
because confidence intervals are complicated to calculate.
In Mr. Wright’s school district, students are allowed to take as much time as they need to finish the final exam in Algebra II. He asked a random sample of 45 of the 600 students who took the exam one year to record the length of time they spent on the exam.
The mean and standard deviation for the 45 students were:
The following year he conducted the same survey and found that the mean time for students finishing was 94.5 minutes.
Using the confidence interval from the previous question, does this provide convincing evidence that the students this year took longer than last year?
The mean time to finish for students this year is outside the confidence interval of plausible values from last year.
The mean time to finish for students this year is within the confidence interval of plausible values.