Lessons 8.1 - 8.3 Content Check Due Wed. 5/8

Last updated almost 2 years ago

21 questions

Note from the author:

Instructions

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Library

Lessons 8.1 - 8.3 Content Check Due Wed. 5/8

Last updated almost 2 years ago

21 questions

Note from the author:

First period, please email me if you find mistakes. But first confirm your method and answer with other students.

Instructions

First period, please email me if you find mistakes. But first confirm your method and answer with other students.

Required

2

Required

2

Required

3

Simon reads a newspaper report claiming that 12% of all adults in the United States are left-handed. He wonders if this figure holds true at the large community college he attends. Simon chooses an SRS of 100 students and finds that 16 of them are left-handed. He uses the data to perform a significance test, where p is the true proportion of lefties at his community college. The test yields a P-value of 0.2184.
Interpret the p-value for this study. Check your notes for Lesson 8.1.

"Assuming.....(null hypothesis is true, use context), there is a ... (p-value probability) of getting... (give the sample results)... or higher/lower purely by chance in random samples of ..."

I will grade this question.

Required

3

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2

Simon reads a newspaper report claiming that 12% of all adults in the United States are left-handed. He wonders if this figure holds true at the large community college he attends. Simon chooses an SRS of 100 students and finds that 16 of them are left-handed. He uses the data to perform a significance test, where p is the true proportion of lefties at his community college. The test yields a P-value of 0.2184. Define and then describe a Type I Error:

Required

2

Simon reads a newspaper report claiming that 12% of all adults in the United States are left-handed. He wonders if this figure holds true at the large community college he attends. Simon chooses an SRS of 100 students and finds that 16 of them are left-handed. He uses the data to perform a significance test, where p is the true proportion of lefties at his community college.
The test yields a P-value of 0.2184. Define and then describe a Type II Error:

Required

2

High blood pressure? A company markets a computerized device for detecting high blood pressure. The device measures an individual’s blood pressure once per hour at a randomly selected time throughout a 12-hour period. Then it calculates the mean systolic (top number) pressure for the sample of measurements.
Based on the sample results, the device performs a test of:
H0: μ = 130 versus Ha: > 130,
where μ is the person’s true mean systolic pressure.
Describe a Type I error in this setting.

Required

2

High blood pressure? A company markets a computerized device for detecting high blood pressure. The device measures an individual’s blood pressure once per hour at a randomly selected time throughout a 12-hour period. Then it calculates the mean systolic (top number) pressure for the sample of measurements.

Based on the sample results, the device performs a test of:
H0: μ = 130 versus Ha: > 130,
where μ is the person’s true mean systolic pressure.

Describe a Type II error in this setting.

Required

1

Based on your answers to #7 & 8, in this scenario, which type of error would be worse?
Type I or Type II?
Explain why or why not.
Use complete sentences that make sense and answer the question.
I will grade this answer.

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3

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4

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1

During the next month, the manager collects data on wait times from a random sample of 250 drive-thru orders, and finds that only 141 of the customers have to wait longer than 2 minutes.
What is the value of the sample proportion from above?
Round to three places past the decimal.

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1

What is the evidence that the store manager has that there might be a difference in wait time?

Hint: what evidence do you have from the sample (what statistic was calculated) that allows you to determine the Ha? It gives you a reason to do the test, it shows there is a difference.
In the past I have told you to compare the sample proportion to the null value.
I will grade this question.

Required

4

But do we have convincing evidence that the proportion of all customers who have to wait longer than 2 minutes has decreased? 
To answer this question, we want to know if it’s likely to get a sample proportion of 0.564 or less by chance alone when the null hypothesis is true. 
In other words, we are looking for a P-value.
To calculate the P-value you will need to find the probability of getting our sample results assuming the null hypothesis is true. 
Use your notes for the formula needed to standardize the statistic into a z-score. 

What is the mean from the null hypothesis? _______ 
What is the standard deviation for the sampling distribution of sample proportions?  Round to 3 places past the decimal._______
What is the standardized test statistic? _______  Round to 2 places past the decimal.

Using the Z chart (blue) what is the probability of getting the sample results, assuming the null hypothesis is true? 
P-value = _______ 

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A recent report claimed that 13% of students typically walk to school. DeAnna thinks that the proportion is higher than 0.13 at her large elementary school. She surveys a random sample of 150 students and finds that 23 typically walk to school.
DeAnna would like to carry out a test at the α = 0.05 significance level.
What is the sample proportion?
Round to 3 places past the decimal.

Required

1

What is the evidence that DeAnna has that there might be a difference in the proportion of students who walk to school?

Hint: what evidence do you have from the sample (what statistic was calculated) that allows you to determine the Ha? It gives you a reason to do the test, it shows there is a difference.
In the past I have told you to compare the sample proportion to the null value.
I will grade this question.

Required

4

But do we have convincing evidence that the proportion of all students at DeAnna's elementary school that walk to school is ? 
To answer this question, we want to know if it’s likely to get a sample proportion of 0.16 or higher by chance alone when the null hypothesis is true. 

In other words, we are looking for a P-value.
To calculate the P-value you will need to find the probability of getting our sample results assuming the null hypothesis is true. 
Use your 8.3 notes for the formula needed to standardize the statistic into a z-score. 

What is the mean from the null hypothesis? _______ 
What is the standard deviation for the sampling distribution of sample proportions?  Round to 3 places past the decimal._______
What is the standardized test statistic?  _______ Round to 2 places past the decimal.

Using the Z chart (blue) what is the probability of getting the sample results, assuming the null hypothesis is true? 
P-Value = _______ Keep in mind: do you want greater than or less than?

Required

3

First period, please email me if you find mistakes. But first confirm your method and answer with other students.

First period, please email me if you find mistakes. But first confirm your method and answer with other students.

Simon reads a newspaper report claiming that 12% of all adults in the United States are left-handed. He wonders if this figure holds true at the large community college he attends.
Simon chooses an SRS of 100 students and records whether each student is right- or left-handed.
What is the parameter of interest?
What is the statistical symbol?

Simon reads a newspaper report claiming that 12% of all adults in the United States are left-handed. He wonders if this figure holds true at the large community college he attends. Simon chooses an SRS of 100 students and records whether each student is right- or left-handed. He found that 16 were left handed.
What is the null and alternative hypothesis?

Simon reads a newspaper report claiming that 12% of all adults in the United States are left-handed. He wonders if this figure holds true at the large community college he attends. Simon chooses an SRS of 100 students and finds that 16 of them are left-handed. He uses the data to perform a significance test, where p is the true proportion of lefties at his community college. The test yields a P-value of 0.2184.
Interpret the p-value for this study. Check your notes for Lesson 8.1.

"Assuming.....(null hypothesis is true, use context), there is a ... (p-value probability) of getting... (give the sample results)... or higher/lower purely by chance in random samples of ..."

I will grade this question.

Simon reads a newspaper report claiming that 12% of all adults in the United States are left-handed. He wonders if this figure holds true at the large community college he attends. Simon chooses an SRS of 100 students and finds that 16 of them are left-handed. He uses the data to perform a significance test, where p is the true proportion of lefties at his community college. The test yields a P-value of 0.2184. What conclusion would you make for the significance level of α = 0.05?
Select 3 correct answers to explain.

Simon reads a newspaper report claiming that 12% of all adults in the United States are left-handed. He wonders if this figure holds true at the large community college he attends. Simon chooses an SRS of 100 students and finds that 16 of them are left-handed. He uses the data to perform a significance test, where p is the true proportion of lefties at his community college. The test yields a P-value of 0.2184. Define and then describe a Type I Error:

Simon reads a newspaper report claiming that 12% of all adults in the United States are left-handed. He wonders if this figure holds true at the large community college he attends. Simon chooses an SRS of 100 students and finds that 16 of them are left-handed. He uses the data to perform a significance test, where p is the true proportion of lefties at his community college.
The test yields a P-value of 0.2184. Define and then describe a Type II Error:

High blood pressure? A company markets a computerized device for detecting high blood pressure. The device measures an individual’s blood pressure once per hour at a randomly selected time throughout a 12-hour period. Then it calculates the mean systolic (top number) pressure for the sample of measurements.
Based on the sample results, the device performs a test of:
H0: μ = 130 versus Ha: > 130,
where μ is the person’s true mean systolic pressure.
Describe a Type I error in this setting.

High blood pressure? A company markets a computerized device for detecting high blood pressure. The device measures an individual’s blood pressure once per hour at a randomly selected time throughout a 12-hour period. Then it calculates the mean systolic (top number) pressure for the sample of measurements.

Based on the sample results, the device performs a test of:
H0: μ = 130 versus Ha: > 130,
where μ is the person’s true mean systolic pressure.

Describe a Type II error in this setting.

Based on your answers to #7 & 8, in this scenario, which type of error would be worse?
Type I or Type II?
Explain why or why not.
Use complete sentences that make sense and answer the question.
I will grade this answer.

The manager of a fast-food restaurant wants to reduce the proportion of drive-thru customers who have to wait longer than 2 minutes to receive their food after placing an order.
Based on store records, the proportion of customers who had to wait longer than 2 minutes was p = 0.63.
To reduce this proportion, the manager assigns an additional employee to assist with drive-thru orders. The manager would like to carry out a significance test at the α = 0.10 significance level.
Select the null and alternative hypothesis below.
Then define the parameter of interest.

Based on store records, the proportion of customers who had to wait longer than 2 minutes was p = 0.63.
To reduce this proportion, the manager assigns an additional employee to assist with drive-thru orders. The manager would like to carry out a significance test at the α = 0.10 significance level.
During the next month, the manager collects data on wait times from a random sample of 250 drive-thru orders, and finds that only 141 of the customers have to wait longer than 2 minutes.
Check if the conditions for performing the significance test are met.
Remember po represents the proportion from the Null Hypothesis.

During the next month, the manager collects data on wait times from a random sample of 250 drive-thru orders, and finds that only 141 of the customers have to wait longer than 2 minutes.
What is the value of the sample proportion from above?
Round to three places past the decimal.

What is the evidence that the store manager has that there might be a difference in wait time?

Hint: what evidence do you have from the sample (what statistic was calculated) that allows you to determine the Ha? It gives you a reason to do the test, it shows there is a difference.
In the past I have told you to compare the sample proportion to the null value.
I will grade this question.

But do we have convincing evidence that the proportion of all customers who have to wait longer than 2 minutes has decreased? 
To answer this question, we want to know if it’s likely to get a sample proportion of 0.564 or less by chance alone when the null hypothesis is true. 
In other words, we are looking for a P-value.
To calculate the P-value you will need to find the probability of getting our sample results assuming the null hypothesis is true. 
Use your notes for the formula needed to standardize the statistic into a z-score. 

What is the mean from the null hypothesis? _______ 
What is the standard deviation for the sampling distribution of sample proportions?  Round to 3 places past the decimal._______
What is the standardized test statistic? _______  Round to 2 places past the decimal.

Using the Z chart (blue) what is the probability of getting the sample results, assuming the null hypothesis is true? 
P-value = _______ 

What is the conclusion for the significance test using a significance level (alpha level) of 10%?

A recent report claimed that 13% of students typically walk to school. DeAnna thinks that the proportion is higher than 0.13 at her large elementary school. She surveys a random sample of 150 students and finds that 23 typically walk to school.
DeAnna would like to carry out a test at the α = 0.05 significance level.

Select the null and alternative hypothesis below.
Then define the parameter of interest.

A recent report claimed that 13% of students typically walk to school. DeAnna thinks that the proportion is higher than 0.13 at her large elementary school. She surveys a random sample of 150 students and finds that 23 typically walk to school.
DeAnna would like to carry out a test at the α = 0.05 significance level.

Check if the conditions for performing the significance test are met.
Remember po represents the proportion from the Null Hypothesis.

A recent report claimed that 13% of students typically walk to school. DeAnna thinks that the proportion is higher than 0.13 at her large elementary school. She surveys a random sample of 150 students and finds that 23 typically walk to school.
DeAnna would like to carry out a test at the α = 0.05 significance level.
What is the sample proportion?
Round to 3 places past the decimal.

What is the evidence that DeAnna has that there might be a difference in the proportion of students who walk to school?

Hint: what evidence do you have from the sample (what statistic was calculated) that allows you to determine the Ha? It gives you a reason to do the test, it shows there is a difference.
In the past I have told you to compare the sample proportion to the null value.
I will grade this question.

But do we have convincing evidence that the proportion of all students at DeAnna's elementary school that walk to school is ? 
To answer this question, we want to know if it’s likely to get a sample proportion of 0.16 or higher by chance alone when the null hypothesis is true. 

In other words, we are looking for a P-value.
To calculate the P-value you will need to find the probability of getting our sample results assuming the null hypothesis is true. 
Use your 8.3 notes for the formula needed to standardize the statistic into a z-score. 

What is the mean from the null hypothesis? _______ 
What is the standard deviation for the sampling distribution of sample proportions?  Round to 3 places past the decimal._______
What is the standardized test statistic?  _______ Round to 2 places past the decimal.

Using the Z chart (blue) what is the probability of getting the sample results, assuming the null hypothesis is true? 
P-Value = _______ Keep in mind: do you want greater than or less than?

What is the conclusion for the significance test using a significance level (alpha level) of 5%?

Simon reads a newspaper report claiming that 12% of all adults in the United States are left-handed. He wonders if this figure holds true at the large community college he attends. 
Simon chooses an SRS of 100 students and records whether each student is right- or left-handed.
What is the parameter of interest?
What is the statistical symbol?

the true proportion of the population

the true mean of the population

p-hat

p

Simon reads a newspaper report claiming that 12% of all adults in the United States are left-handed. He wonders if this figure holds true at the large community college he attends. Simon chooses an SRS of 100 students and records whether each student is right- or left-handed. He found that 16 were left handed.
What is the null and alternative hypothesis?

Simon reads a newspaper report claiming that 12% of all adults in the United States are left-handed. He wonders if this figure holds true at the large community college he attends. Simon chooses an SRS of 100 students and finds that 16 of them are left-handed. 
He uses the data to perform a significance test, where p is the true proportion of lefties at his community college. 
The test yields a P-value of 0.2184. 
What conclusion would you make for the significance level of α = 0.05?
Select 3 correct answers to explain.

Fail to reject the Ho

We do not have convincing evidence that the proportion of left handed students is not 12%.

Reject the Ho

p-value > alpha level of 0.05

p-value < alpha level of 0.05

We have convincing evidence that the proportion of left handed students is not 12%.

Type I Error: Fail to reject the Null Hypothesis when it really isn't true.

Type II Error: Determine that the true proportion of left handed students is not 12% when really it is.

Type II Error: Reject the Null Hypothesis when it really is true.

Type I Error: Determine that the person's systolic pressure is greater than 130 (high blood pressure) when really it is not.

Type I Error: Determine that the person's systolic pressure is equal to 130 (normal blood pressure) when really it is not.

Type I Error: Reject the Null Hypothesis when it really is true.

Type II Error: Determine that the person's systolic pressure is greater than 130 (high blood pressure) when really it is not.

Type II Error: Determine that the person's systolic pressure is equal to 130(normal blood pressure) when really it is higher than 130.

Type II Error: Reject the Null Hypothesis when it really is true.

Type II Error: Fail to reject the Null Hypothesis when really it is not true

The manager of a fast-food restaurant wants to reduce the proportion of drive-thru customers who have to wait longer than 2 minutes to receive their food after placing an order. 
Based on store records, the proportion of customers who had to wait longer than 2 minutes was p = 0.63. 
To reduce this proportion, the manager assigns an additional employee to assist with drive-thru orders. The manager would like to carry out a significance test at the α = 0.10 significance level.
Select the null and alternative hypothesis below. 
Then define the parameter of interest.

P= the true proportion of customers who had to wait longer than 2 minutes

P= the true proportion of customers who waited less than 2 minutes

Based on store records, the proportion of customers who had to wait longer than 2 minutes was p = 0.63.
To reduce this proportion, the manager assigns an additional employee to assist with drive-thru orders. The manager would like to carry out a significance test at the α = 0.10 significance level.
During the next month, the manager collects data on wait times from a random sample of 250 drive-thru orders, and finds that only 141 of the customers have to wait longer than 2 minutes. 
Check if the conditions for performing the significance test are met.
Remember po represents the proportion from the Null Hypothesis.

n(1-P) > 10 because 250(0.37) = 92.5

Large Counts condition has been met

n(P) > 10 because 250(0.63) = 157.5

n(P) > 10 because 141(0.63) = 88.83

Random sample has been met because 'a random sample of 250 drive thru orders' used.

Random sample has been met because the manager used 'a SRS of 250 orders'.

n(1-P) > 10 because 141(1-0.63) = 157.5

Large Counts condition has not been met

Random sample was not met, it is not mentioned in the problem.

What is the conclusion for the significance test using a significance level (alpha level) of 10%?

we reject Ho

we fail to reject H0

We do not have convincing evidence that the true proportion of drive-thru customers who have to wait more than 2 minutes is now less than 0.63.

Because the P-value of 0.0166 is greater than α = 0.10

We have convincing evidence that the true proportion of drive-thru customers who have to wait more than 2 minutes is now less than 0.63.

Because the P-value of 0.0166 is less than α = 0.10 

A recent report claimed that 13% of students typically walk to school. DeAnna thinks that the proportion is higher than 0.13 at her large elementary school. She surveys a random sample of 150 students and finds that 23 typically walk to school. 
DeAnna would like to carry out a test at the α = 0.05 significance level.

Select the null and alternative hypothesis below. 
Then define the parameter of interest.

P= the true proportion of how students at her elementary school typically get to school.

P= the true proportion of all students at her elementary school who typically walk to school.

A recent report claimed that 13% of students typically walk to school. DeAnna thinks that the proportion is higher than 0.13 at her large elementary school. She surveys a random sample of 150 students and finds that 23 typically walk to school.
DeAnna would like to carry out a test at the α = 0.05 significance level.

Check if the conditions for performing the significance test are met.
Remember po represents the proportion from the Null Hypothesis.

Random sample has been met because the manager used 'a SRS of 150 students'.

Random sample was not met, it is not mentioned in the problem.

Large Counts condition has not been met

n(Po) > 10 because 127(0.13) = 16.51

n(1-Po) > 10 because 127(0.87) = 110.49

Large Counts condition has been met

n(1-Po) > 10 because 150(0.87) = 130.5

n(Po) > 10 because 150(0.13) = 19.5

Random sample has been met because 'a random sample of 150 students' used.

What is the conclusion for the significance test using a significance level (alpha level) of 5%?

Because the P-value of 0.1977 is less than α = 0.05 

We do not have convincing evidence that the true proportion of students at DeAnna's elementary who walk to school is greater than 13%.

Because the P-value of 0.1977 is greater than α = 0.05

We have convincing evidence that the true proportion of students at DeAnna's elementary who walk to school is greater than 13%.

we reject Ho

we fail to reject H0

Lessons 8.1 - 8.3 Content Check Due Wed. 5/8

Lessons 8.1 - 8.3 Content Check Due Wed. 5/8

Based on your answers to #7 & 8, in this scenario, which type of error would be worse?Type I or Type II?Explain why or why not.Use complete sentences that make sense and answer the question.I will grade this answer.

During the next month, the manager collects data on wait times from a random sample of 250 drive-thru orders, and finds that only 141 of the customers have to wait longer than 2 minutes.What is the value of the sample proportion from above?Round to three places past the decimal.

Based on your answers to #7 & 8, in this scenario, which type of error would be worse?Type I or Type II?Explain why or why not.Use complete sentences that make sense and answer the question.I will grade this answer.

During the next month, the manager collects data on wait times from a random sample of 250 drive-thru orders, and finds that only 141 of the customers have to wait longer than 2 minutes.What is the value of the sample proportion from above?Round to three places past the decimal.

What is the conclusion for the significance test using a significance level (alpha level) of 10%?

What is the conclusion for the significance test using a significance level (alpha level) of 5%?

Based on your answers to #7 & 8, in this scenario, which type of error would be worse?
Type I or Type II?
Explain why or why not.
Use complete sentences that make sense and answer the question.
I will grade this answer.

During the next month, the manager collects data on wait times from a random sample of 250 drive-thru orders, and finds that only 141 of the customers have to wait longer than 2 minutes.
What is the value of the sample proportion from above?
Round to three places past the decimal.

Based on your answers to #7 & 8, in this scenario, which type of error would be worse?
Type I or Type II?
Explain why or why not.
Use complete sentences that make sense and answer the question.
I will grade this answer.

During the next month, the manager collects data on wait times from a random sample of 250 drive-thru orders, and finds that only 141 of the customers have to wait longer than 2 minutes.
What is the value of the sample proportion from above?
Round to three places past the decimal.