2023 Spring Semester Exam Review

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Ch. 5 Normal Distribution
For the first group of questions - use your half sheet on the 68-95-99.7 Rule (Empirical Rule).
A new group of IQ tests are standardized to a Normal Model, N(110,14).

Answer:
What percent of the data values fall between the IQ's of 96 and 124?

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Using the Normal Distribution from #1:
How many standard deviations from the mean is the top 16% of the IQ scores?  _______ 

What is the IQ score needed to be in the top 16%?  _______ 

What percentile would this be? _______ 
Hint: remember, percentiles are the percent to the LEFT of a given point

Then shade the corresponding area under the normal curve in the 'show your work' area below.

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Using the Normal Distribution from #1:
How many standard deviations is the top 2.5% from the mean?  _______ 

What is the IQ score needed to be in the top 2.5%?  _______ 

What percentile would this be? _______ 
Hint: remember, percentiles are the percent to the LEFT of a given point

Then shade the corresponding area under the normal curve in the 'show your work' area below,.

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Using the Normal Distribution from #1:
What percent of the IQ scores are 82 or lower?  _______ 

What percent of the IQ scores are 124 or lower?  _______ 

What percent of the IQ scores are 68 or lower? _______ 
Hint: remember, percentiles are the percent to the LEFT of a given point

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Fill in the blanks:
Using the normal distribution model:
N(3.25, 1.4)  Mean=  _______      Standard Deviation= _______ 

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What does the z-score mean?
Suppose that a Normal model described student scores in a history class.
Francisco has a standardized score (z-score) of +2.5.

This means that Francisco’s score...

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If the heights of 6th graders at Danville Middle School follow a normal distribution with the mean height of 58.5 inches and the standard deviation of 2.45 inches, give the notation for the Normal model.
Use the format: N(mean, std dev)

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The Delorean speeds from 'Back To The Future' follow a Normal Distribution, with the model N(80, 7.7).
What percent of the runs will give the Delorean a speed less than 68.45 mph?
First: what is the z-score for 68.45? _______  Enter all decimal places for this one.
Use the z-score formula: 


Second: answer,
what is the proportion of runs that will give the Delorean a speed less than 68.45 mph? _______ 

THEN: Shade in the probability area that you are calculating in the 'show your work' area.

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What percent of the runs will give the Delorean a speed greater than 85 mph?
First: what is the z-score for the speed? _______ 
Remember to round to two places.



Second: be careful, I am asking for the percent GREATER than 85 mph, think about what you need to do, collaborate! 
What is the proportion of speeds less than 85 mph? _______ 
              
Third: What do you need to do with the value to find the proportion higher?
                                                                   Add, subtract, multiply or divide? _______ 

           What percent of the runs will give the Delorean a speed greater than 85 mph? _______ 
        Hint: the area to the left and the right need to add to 1.0, the total area under the curve.
THEN: Shade in the probability area that you are calculating in the 'show your work' area.

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What percent of the runs will give the Delorean a speed between 70 and 95 mph?
Remember it follows the model:  N(80, 7.7).
First: what is the z-score for the speed of 70 mph? _______   
Remember to round to two places.
          what is the z-score for the speed of 95 mph? _______ 



Second: what proportion corresponds to 70 mph? _______ 
               what proportion corresponds to 95 mph? _______ 

Third: answer, what will you do with the two proportions? 
                           Add, subtract, multiply or divide? _______ 
What percent of the runs will give the Delorean a speed between 70 and 95 mph? _______ 
Hint: you want the area BETWEEN the two points, you will need to subtract!

THEN: Shade in the probability area that you are calculating in the 'show your work' area.

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High levels of cholesterol in the blood increase the risk of heart disease. For teenage boys, the distribution of blood cholesterol is approximately normal with mean μ = 151.6 milligrams of cholesterol per deciliter of blood (mg/dl) and standard deviation σ = 25 mg/dl.

What is the Normal model for this situation?
Use the format: N(mean, std. dev.)

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What proportion of teen boys have cholesterol levels less than 100 mg/dl?
First: what is the z-score for 100 mg/dl? _______  Remember to round to two places.
                       
Second: What is the proportion? _______ 

THEN:  Shade in the probability area that you are calculating in the 'show your work' area.

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Cholesterol levels of 200 or higher are considered high for teenagers. 
What percent of teen boys have high cholesterol?
First: what is the z-score for 200 mg/dl? _______ 



Second: What is the proportion to the left of the z-score? _______ 
               What do you need to do with the value to find the proportion higher?
                              Add, subtract, multiply or divide?  _______ 
Third: what is the proportion GREATER than 200 mg/dl? _______ 

THEN: Shade in the probability area that you are calculating in the 'show your work' area.

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Cholesterol levels between 170 mg/dl and 200 mg/dl are considered borderline high for teenagers. What percent of teen boys have borderline high cholesterol levels?
First: what is the z-score for 170 mg/dl?  _______ 
          what is the z-score for 200 mg/dl?  _______ 


Second: What is the proportion to the left of 170?  _______ 
               What is the proportion to the left of 200?  _______ 

Third: what will you do with the two proportions? Add, subtract, multiply or divide? _______ 
            what percent of teen boys have borderline high cholesterol levels? _______ 

THEN: Shade in the probability area that you are calculating in the 'show your work' area.

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People with z-scores greater than 2.5 on an IQ test are considered as geniuses.
IQ tests have a score of a mean of 100 and SD of 16 points.

What is the cut off score to show someone is a genius? Hint: use the z-score.

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Chapter 6 Sampling Distributions
A study of voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election. Election records show that only 56% of registered voters voted in the election.
Match up the following statements about these percentages?

Draggable item		Corresponding Item
All voters		Parameter
72%		Statistic

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At a high school, 85% of students are right-handed. 
Let X = the number of students who are right-handed in a random sample of 10 students from the school. 
What is the sample size? n= _______ 
What is the mean of the sampling distribution?  _______  enter as a proportion, not a percent.
What is the standard deviation of the sampling distribution?  _______  Round to three places past the decimal point.

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Scores on the mathematics part of the SAT exam in a recent year followed a normal distribution with mean 515 and standard deviation 114.
You choose an SRS of 100 students and calculate mean SAT Math score.
Match up the following for this situation.

Draggable item		Corresponding Item
100		sample size (n)
515

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In a congressional district, 52% of the registered voters are Democrats. An SRS of 100 voters is going to be polled.
What is the mean of the sampling distribution of the sample proportion of democrat voters? _______ 

What is the standard deviation of the sampling distribution of the sample proportion of democrat voters? _______ Round to two places past the decimal.

What is the probability of getting less than 50% Democrats in a random sample of size 100?
_______  
Keep your answer as the decimal proportion, keep all decimal places (there will be four)

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Use the information in the previous question.
What is the probability of getting a sample of 100 registered voters with more than 65% democrats?
Keep all decimals.

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The amount that households pay service providers for access to the Internet varies quite a bit, but the mean monthly fee is $48 and the standard deviation is $20. 
The distribution is not normal: Many households pay a base rate for low-speed access, but some pay much more for faster connections so the distribution is strongly right skewed. 

A sample survey asks an SRS of 500 households with Internet access how much they pay per month. Let X-bar be the mean amount paid by the members of the sample.

Calculate the mean and standard deviation of the sampling distribution of the sample means. 
Sampling distribution sample mean = _______ 
Sampling distribution of sample means standard deviation = _______  
Round to three places past the decimal.

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Use the information in the previous two questions:
In a sampling distribution, find the probability that the average amount paid by the sample of households exceeds $50.

z-score = _______  round to two places past the decimal

Probability = _______ Keep the probability as a decimal proportion

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Use the information from the previous 3 questions:
In a sampling distribution, what is the probability that the average amount paid by the sample of households is less than $46.50.
z-score = _______   round to two places past the decimal

Probability = _______ Keep your answer as a decimal proportion.

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In a recent year, 73% of first-year college students identified “being very well-off financially” as an important personal goal.
A state university finds that 132 of an SRS of 200 of its first-year students say that this goal is important.
Construct a 95% confidence interval for the true proportion of all first-year students at the university who would identify being well-off as an important personal goal.
Check your formula chart, round to three places past the decimal.
Lower bound: _______ 
Upper bound: _______ 

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Based on your previous answer:
Explain what the confidence interval tells you about whether the national value of 73% holds at this university.

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Melissa and Madeline love pepperoni pizza, but sometimes they are disappointed with the small number of pepperonis on their pizza. 
To investigate, they went to their favorite pizza restaurant at 10 random times during the week and ordered a large pepperoni pizza. Here are the number of pepperonis on each pizza.
47  36  25  37  46  36  49  32  32  34
Statsmedic.com gives an average of 37.4 pepperonis and a Sx= 7.662 
Construct and interpret a 95% confidence interval for the true mean number of pepperonis on a large pizza at this restaurant.

Check your formula chart, round to three places past the decimal.
Lower bound: _______ 
Upper bound: _______ 

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Based on your previous answer:
Explain what the confidence interval tells you about whether the manager's requirement of 40 pepperonis on each large pizza is being followed.

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Chapter 8
Identify the types of Errors when performing a significance test:

Ho is TRUE and you REJECT Ho
Ha is TRUE and you FAIL TO REJECT Ho
Ha is TRUE and you REJECT Ho
Ho is TRUE and you FAIL TO REJECT Ho

Type I Error
Type II Error

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Flu vaccine A drug company has developed a new vaccine for preventing the flu. The company claims that less than 5% of adults who use its vaccine will get the flu. To test the claim, researchers give the vaccine to a random sample of 1000 adults. Of these, 43 get the flu.
Ho: p > 0.05
Ha: p < 0.05

What is a Type I Error in this setting?
What is a Type II Error in this setting?
Which would be a more serious mistake in this setting—a Type I error or a Type II error?

Deciding that less than 5% of adults who use the vaccine will get the flu and less than 5% actually get the flu.
Deciding that 5% or more of adults who use the vaccine will get the flu, so the vaccine is not used and less than 5% will actually get the flu.
Deciding that 5% or more of adults who use the vaccine will get the flu so the vaccine is not used and 5% or more will actually get the flu.
Deciding that less than 5% of adults who use the vaccine will get the flu, so the vaccine is used and 5% or more will actually get the flu.

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Zenon decided to investigate whether students at his school prefer name-brand potato chips to generic potato chips. He randomly selected 50 students and had each student try both types of chips, in random order. 
Overall, 34 of the 50 students preferred the name-brand chips. 
Zenon wants to perform a test at the α = 0.05 significance level of 
H0: p = 0.5 versus Ha: p > 0.5, 
where p = the true proportion of all students at his school who prefer name-brand chips.

Sample proportion = _______ 
Sampling distribution standard error = _______ round to three places past the decimal
Standardized test statistic (z statistic) = _______ round to two places past the decimal
What is the p value for having this sample proportion given the null value is true? _______ Keep all places past the decimal.

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Suppose that you want to perform a test at the α = 0.10 significance level of
H0 : μ = 5
Ha: μ ≠ 5
A random sample of size n = 20 from the population of interest yields  mean= 5.21 and 
Sx = 0.79. 
Calculate the standard error for the sampling distribution: _______ round to 3 places past the decimal
Calculate the standardized test statistic: _______ round to 3 places past the decimal
Degrees of freedom = _______ 
Give the lower and upper probabilities for the P-value interval: _______ - _______ 

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2023 Spring Semester Exam Review

Ch. 5 Normal Distribution
For the first group of questions - use your half sheet on the 68-95-99.7 Rule (Empirical Rule).
A new group of IQ tests are standardized to a Normal Model, N(110,14).

Answer:
What percent of the data values fall between the IQ's of 96 and 124?

What does the z-score mean?
Suppose that a Normal model described student scores in a history class.
Francisco has a standardized score (z-score) of +2.5.

This means that Francisco’s score...

If the heights of 6th graders at Danville Middle School follow a normal distribution with the mean height of 58.5 inches and the standard deviation of 2.45 inches, give the notation for the Normal model.
Use the format: N(mean, std dev)

People with z-scores greater than 2.5 on an IQ test are considered as geniuses.
IQ tests have a score of a mean of 100 and SD of 16 points.

What is the cut off score to show someone is a genius? Hint: use the z-score.

Scores on the mathematics part of the SAT exam in a recent year followed a normal distribution with mean 515 and standard deviation 114.
You choose an SRS of 100 students and calculate mean SAT Math score.
Match up the following for this situation.

Use the information in the previous question.
What is the probability of getting a sample of 100 registered voters with more than 65% democrats?
Keep all decimals.

Based on your previous answer:
Explain what the confidence interval tells you about whether the national value of 73% holds at this university.

Based on your previous answer:
Explain what the confidence interval tells you about whether the manager's requirement of 40 pepperonis on each large pizza is being followed.

Chapter 8
Identify the types of Errors when performing a significance test:

Ch. 5 Normal Distribution
For the first group of questions - use your half sheet on the 68-95-99.7 Rule (Empirical Rule).
A new group of IQ tests are standardized to a Normal Model, N(110,14).

Answer:
What percent of the data values fall between the IQ's of 96 and 124?

What does the z-score mean?
Suppose that a Normal model described student scores in a history class.
Francisco has a standardized score (z-score) of +2.5.

This means that Francisco’s score...

If the heights of 6th graders at Danville Middle School follow a normal distribution with the mean height of 58.5 inches and the standard deviation of 2.45 inches, give the notation for the Normal model.
Use the format: N(mean, std dev)

People with z-scores greater than 2.5 on an IQ test are considered as geniuses.
IQ tests have a score of a mean of 100 and SD of 16 points.

What is the cut off score to show someone is a genius? Hint: use the z-score.

A polling organization wants to estimate the proportion of voters who favor a new law banning smoking in public buildings.
The organization decides to increase the size of its random sample of voters from about 1500 people to about 4000 people right before an election.
The effect of this is to

The central limit theorem is important in statistics because it allows us to use the normal distribution to find probabilities involving the sample mean if the

Scores on the mathematics part of the SAT exam in a recent year followed a normal distribution with mean 515 and standard deviation 114.
You choose an SRS of 100 students and calculate mean SAT Math score.
Match up the following for this situation.

Use the information in the previous question.
What is the probability of getting a sample of 100 registered voters with more than 65% democrats?
Keep all decimals.

Using the information above, suppose an actual sample of 100 of the registered voters actually resulted in 65% democrats. Would you have convincing evidence that the estimated 52% democrat voters was incorrect? Explain.

Use the information from the previous question:
What is the shape of the population and the sampling distribution of x-bar ? Justify.

Chapter 7: Confidence Intervals
Tim purchased a random sample of clementines at a local grocery store. The 95% confidence interval for the mean weight of all clementines at this store is 76.6 grams to 90.1 grams. Interpret this confidence interval.

Based on your previous answer:
Explain what the confidence interval tells you about whether the national value of 73% holds at this university.

Based on your previous answer:
Explain what the confidence interval tells you about whether the manager's requirement of 40 pepperonis on each large pizza is being followed.

Chapter 8
Identify the types of Errors when performing a significance test:

What is the conclusion based on the P value above?

Based on an alpha level of 0.10, give the conclusion for the significance test.

2023 Spring Semester Exam Review

2023 Spring Semester Exam Review

Ch. 5 Normal DistributionFor the first group of questions - use your half sheet on the 68-95-99.7 Rule (Empirical Rule).A new group of IQ tests are standardized to a Normal Model, N(110,14). Answer:What percent of the data values fall between the IQ's of 96 and 124?

What does the z-score mean?Suppose that a Normal model described student scores in a history class. Francisco has a standardized score (z-score) of +2.5. This means that Francisco’s score...

If the heights of 6th graders at Danville Middle School follow a normal distribution with the mean height of 58.5 inches and the standard deviation of 2.45 inches, give the notation for the Normal model.Use the format: N(mean, std dev)

People with z-scores greater than 2.5 on an IQ test are considered as geniuses. IQ tests have a score of a mean of 100 and SD of 16 points. What is the cut off score to show someone is a genius? Hint: use the z-score.

Scores on the mathematics part of the SAT exam in a recent year followed a normal distribution with mean 515 and standard deviation 114. You choose an SRS of 100 students and calculate mean SAT Math score. Match up the following for this situation.

Use the information in the previous question. What is the probability of getting a sample of 100 registered voters with more than 65% democrats?Keep all decimals.

Based on your previous answer:Explain what the confidence interval tells you about whether the national value of 73% holds at this university.

Based on your previous answer:Explain what the confidence interval tells you about whether the manager's requirement of 40 pepperonis on each large pizza is being followed.

Chapter 8Identify the types of Errors when performing a significance test:

Ch. 5 Normal DistributionFor the first group of questions - use your half sheet on the 68-95-99.7 Rule (Empirical Rule).A new group of IQ tests are standardized to a Normal Model, N(110,14). Answer:What percent of the data values fall between the IQ's of 96 and 124?

What does the z-score mean?Suppose that a Normal model described student scores in a history class. Francisco has a standardized score (z-score) of +2.5. This means that Francisco’s score...

If the heights of 6th graders at Danville Middle School follow a normal distribution with the mean height of 58.5 inches and the standard deviation of 2.45 inches, give the notation for the Normal model.Use the format: N(mean, std dev)

People with z-scores greater than 2.5 on an IQ test are considered as geniuses. IQ tests have a score of a mean of 100 and SD of 16 points. What is the cut off score to show someone is a genius? Hint: use the z-score.

A polling organization wants to estimate the proportion of voters who favor a new law banning smoking in public buildings. The organization decides to increase the size of its random sample of voters from about 1500 people to about 4000 people right before an election. The effect of this is to

The central limit theorem is important in statistics because it allows us to use the normal distribution to find probabilities involving the sample mean if the

Scores on the mathematics part of the SAT exam in a recent year followed a normal distribution with mean 515 and standard deviation 114. You choose an SRS of 100 students and calculate mean SAT Math score. Match up the following for this situation.

Use the information in the previous question. What is the probability of getting a sample of 100 registered voters with more than 65% democrats?Keep all decimals.

Using the information above, suppose an actual sample of 100 of the registered voters actually resulted in 65% democrats. Would you have convincing evidence that the estimated 52% democrat voters was incorrect? Explain.

Use the information from the previous question:What is the shape of the population and the sampling distribution of x-bar ? Justify.

Chapter 7: Confidence IntervalsTim purchased a random sample of clementines at a local grocery store. The 95% confidence interval for the mean weight of all clementines at this store is 76.6 grams to 90.1 grams. Interpret this confidence interval.

Based on your previous answer:Explain what the confidence interval tells you about whether the national value of 73% holds at this university.

Based on your previous answer:Explain what the confidence interval tells you about whether the manager's requirement of 40 pepperonis on each large pizza is being followed.

Chapter 8Identify the types of Errors when performing a significance test:

What is the conclusion based on the P value above?

Based on an alpha level of 0.10, give the conclusion for the significance test.

Ch. 5 Normal Distribution
For the first group of questions - use your half sheet on the 68-95-99.7 Rule (Empirical Rule).
A new group of IQ tests are standardized to a Normal Model, N(110,14).

Answer:
What percent of the data values fall between the IQ's of 96 and 124?

What does the z-score mean?
Suppose that a Normal model described student scores in a history class.
Francisco has a standardized score (z-score) of +2.5.

This means that Francisco’s score...

If the heights of 6th graders at Danville Middle School follow a normal distribution with the mean height of 58.5 inches and the standard deviation of 2.45 inches, give the notation for the Normal model.
Use the format: N(mean, std dev)

People with z-scores greater than 2.5 on an IQ test are considered as geniuses.
IQ tests have a score of a mean of 100 and SD of 16 points.

What is the cut off score to show someone is a genius? Hint: use the z-score.

Scores on the mathematics part of the SAT exam in a recent year followed a normal distribution with mean 515 and standard deviation 114.
You choose an SRS of 100 students and calculate mean SAT Math score.
Match up the following for this situation.

Use the information in the previous question.
What is the probability of getting a sample of 100 registered voters with more than 65% democrats?
Keep all decimals.

Based on your previous answer:
Explain what the confidence interval tells you about whether the national value of 73% holds at this university.

Based on your previous answer:
Explain what the confidence interval tells you about whether the manager's requirement of 40 pepperonis on each large pizza is being followed.

Chapter 8
Identify the types of Errors when performing a significance test:

Ch. 5 Normal Distribution
For the first group of questions - use your half sheet on the 68-95-99.7 Rule (Empirical Rule).
A new group of IQ tests are standardized to a Normal Model, N(110,14).

Answer:
What percent of the data values fall between the IQ's of 96 and 124?

What does the z-score mean?
Suppose that a Normal model described student scores in a history class.
Francisco has a standardized score (z-score) of +2.5.

This means that Francisco’s score...

If the heights of 6th graders at Danville Middle School follow a normal distribution with the mean height of 58.5 inches and the standard deviation of 2.45 inches, give the notation for the Normal model.
Use the format: N(mean, std dev)

People with z-scores greater than 2.5 on an IQ test are considered as geniuses.
IQ tests have a score of a mean of 100 and SD of 16 points.

What is the cut off score to show someone is a genius? Hint: use the z-score.

A polling organization wants to estimate the proportion of voters who favor a new law banning smoking in public buildings.
The organization decides to increase the size of its random sample of voters from about 1500 people to about 4000 people right before an election.
The effect of this is to

Scores on the mathematics part of the SAT exam in a recent year followed a normal distribution with mean 515 and standard deviation 114.
You choose an SRS of 100 students and calculate mean SAT Math score.
Match up the following for this situation.

Use the information in the previous question.
What is the probability of getting a sample of 100 registered voters with more than 65% democrats?
Keep all decimals.

Use the information from the previous question:
What is the shape of the population and the sampling distribution of x-bar ? Justify.

Chapter 7: Confidence Intervals
Tim purchased a random sample of clementines at a local grocery store. The 95% confidence interval for the mean weight of all clementines at this store is 76.6 grams to 90.1 grams. Interpret this confidence interval.

Based on your previous answer:
Explain what the confidence interval tells you about whether the national value of 73% holds at this university.

Based on your previous answer:
Explain what the confidence interval tells you about whether the manager's requirement of 40 pepperonis on each large pizza is being followed.

Chapter 8
Identify the types of Errors when performing a significance test: