Lessons 7.3-7.6 Content Check

Instructions

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).

Required

2

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?

Required

7

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.

Draggable item		Corresponding Item
part/whole		formula for calculating a proportion
1 sample z interval for p		Sample statistic
p		Population parameter we are estimating
0.33		p-hat value
p-hat		not the p-hat value
1 sample t interval for mu		Inference method we will use
0.66		Inference method we will not use

Required

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.
Are the conditions met for creating a 95% Confidence Interval?

Required

3

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? _______  

Required

2

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?

Required

2

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?

Required

2

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.

Required

5

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?  _______ 

Required

2

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.

Required

5

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?

Required

2

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?

Required

7

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:

Draggable item		Corresponding Item
part/whole		formula for calculating a proportion
p-hat		Sample statistic
1 sample z interval for p		Population parameter we are estimating
0.11		p-hat value
p		not the p-hat value
0.19		Inference method we will use
1 sample t interval for mu		Inference method we will not use

Required

6

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:

Draggable item		Corresponding Item
172(1-0.19)		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)
19		value of n*p-hat
An SRS of 172 undergraduates was conducted		value of n*(1- p-hat)
172(1-0.11)		incorrect answer

Required

4

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? _______  

Required

2

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?

Required

3

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 _______

Required

4

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 = _______ 

Required

2

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?

Lessons 7.3-7.6 Content Check

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?

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?

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?

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?

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?

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?

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?

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?