Question 1

Using the same sample data, the margin of error for an 80% confidence interval is __________ than the margin of error for a 90% confidence interval.

Accepted Answer

The answer of Using the same sample data, the margin...

Question 2

For Questions use the following narrative
Narrative: Oranges
Suppose a shipment of oranges is advertised to weigh 5 pounds per bag.We know that not every bag can contain exactly 5 pounds of oranges.We decide to take a random sample of 100 bags of oranges and find out what they tell us about the population of all bags in this shipment.We are only interested in whether or not the bags are underweight, so each bag is weighed and counted as underweight if it weighs less than 5 pounds.Five bags in our sample of 100 were found to be underweight.
-{Oranges narrative} Suppose the grocery store who ordered the oranges will reject the shipment if they believe, based on these sample results, that more than 10% of the bags in the entire truckload are underweight.Based on our sample, will they have to return this shipment? Explain your answer.

Accepted Answer

The answer of For Questions use the following narrative
Narrative: Oranges
Suppose...

Question 3

For Questions use the following narrative
Narrative: Oranges
Suppose a shipment of oranges is advertised to weigh 5 pounds per bag.We know that not every bag can contain exactly 5 pounds of oranges.We decide to take a random sample of 100 bags of oranges and find out what they tell us about the population of all bags in this shipment.We are only interested in whether or not the bags are underweight, so each bag is weighed and counted as underweight if it weighs less than 5 pounds.Five bags in our sample of 100 were found to be underweight.
-{Oranges narrative} What is the margin of error for a 95% confidence interval for the proportion of bags in the shipment that are underweight?

Accepted Answer

The answer of For Questions use the following narrative
Narrative: Oranges
Suppose...

Question 4

The formula for calculating a confidence interval for a population proportion is based on the rule of sample proportions, which has assumptions that need to be met.What is the most important assumption that you need to check before applying the confidence interval formula to a sample proportion?

Accepted Answer

The answer of The formula for calculating a confidence interval...

Question 5

Sampling methods and confidence intervals are routinely used for financial audits of large companies.Which of the following is an advantage of doing it this way, versus having a complete audit of all records?

Accepted Answer

Sampling methods and confidence intervals offer several advantages over complete audits. They are cheaper because auditing a sample requires fewer resources than auditing every single record. Additionally, because auditors are dealing with a smaller dataset, they can afford to be more meticulous in their examination, potentially leading to a more careful audit. Furthermore, a well-designed sampling method, when executed with precision, can indeed yield more accurate estimates than a complete audit that might be conducted with less attention to detail due to the sheer volume of data.

Question 6

Using one divided by the square root of the sample size is known as a 'conservative' formula for the margin of error for a sample proportion.Explain what that means.

Accepted Answer

The answer of Using one divided by the square root...

Question 7

In which of the following situations can you construct a confidence interval for the population proportion with only what is given?

Accepted Answer

For constructing a confidence interval for the population proportion, we need the sample proportion and either the margin of error or the sample size. Option A gives us both of these pieces of information. Option B only gives us the sample proportion and sample size, but we can use the sample size to calculate the margin of error. Option C gives us the two counts (with the trait of interest and without), but we would also need the sample size to calculate the sample proportion and the margin of error. Therefore, option D gives us all the necessary information to construct a confidence interval.

Question 8

To obtain a 99.7% (virtually all-encompassing) confidence interval for the true population proportion, you would add and subtract about __________ standard deviations to/from the sample proportion.

Accepted Answer

The answer of To obtain a 99.7% (virtually all-encompassing) confidence...

Question 9

In which of the following situations can a confidence interval provide useful information for making a decision?

Accepted Answer

Confidence intervals can provide useful information in all the given situations by estimating the range within which the true parameter (e.g., percentage or proportion) lies with a certain level of confidence. This can help in making decisions based on statistical evidence regarding the accuracy of financial entries, the proportion of married couples with taller wives, or the existence of ESP.

Question 10

Which of the following statements is true regarding a 95% confidence interval? Assume numerous large samples are taken from the population.

Accepted Answer

All of the statements are true regarding a 95% confidence interval.

Question 11

For Questions use the following narrative
Narrative: Oranges
Suppose a shipment of oranges is advertised to weigh 5 pounds per bag.We know that not every bag can contain exactly 5 pounds of oranges.We decide to take a random sample of 100 bags of oranges and find out what they tell us about the population of all bags in this shipment.We are only interested in whether or not the bags are underweight, so each bag is weighed and counted as underweight if it weighs less than 5 pounds.Five bags in our sample of 100 were found to be underweight.
-{Oranges narrative} What percentage of all the bags in the entire shipment do you think are underweight? Give the most complete answer you can.
Acceptable

Accepted Answer

The answer of For Questions use the following narrative
Narrative: Oranges
Suppose...

Quiz 20: Estimating Proportions With Confidence

Using the same sample data, the margin of error for an 80% confidence interval is __________ than the margin of error for a 90% confidence interval.

The formula for calculating a confidence interval for a population proportion is based on the rule of sample proportions, which has assumptions that need to be met.What is the most important assumption that you need to check before applying the confidence interval formula to a sample proportion?

Sampling methods and confidence intervals are routinely used for financial audits of large companies.Which of the following is an advantage of doing it this way, versus having a complete audit of all records?

Using one divided by the square root of the sample size is known as a 'conservative' formula for the margin of error for a sample proportion.Explain what that means.

In which of the following situations can you construct a confidence interval for the population proportion with only what is given?

To obtain a 99.7% (virtually all-encompassing) confidence interval for the true population proportion, you would add and subtract about __________ standard deviations to/from the sample proportion.

In which of the following situations can a confidence interval provide useful information for making a decision?

Which of the following statements is true regarding a 95% confidence interval? Assume numerous large samples are taken from the population.