Question 1

For Questions , use the following narrative
Narrative: Test scores
Suppose that test scores on a particular exam have a mean of 77 and standard deviation of 5, and that they have a bell-shaped curve.
-{Test scores narrative} Suppose you take a single random sample of size 100 people from this population.What is the chance that their average test score will be above 77?

Accepted Answer

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Narrative:...

Question 2

For Questions , use the following narrative
Narrative: Test scores
Suppose that test scores on a particular exam have a mean of 77 and standard deviation of 5, and that they have a bell-shaped curve.
-{Test scores narrative} Suppose you randomly select a single individual from this population.Where would you expect his/her test score to fall?

Accepted Answer

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Question 3

If numerous large random samples or repetitions of the same size are taken from a population, the frequency curve made from means from the various samples will have what approximate shape?

Accepted Answer

According to the Central Limit Theorem, the frequency curve made from means from numerous large random samples or repetitions of the same size taken from a population will have a bell-shaped curve, also known as a normal distribution. This is because the means will tend to cluster around the population mean, resulting in a symmetrical distribution with most of the data falling close to the mean.

Question 4

In which of the following situations does the rule for sample proportions apply?

Accepted Answer

The rule for sample proportions applies in situations where we are interested in the percentage or proportion of a certain characteristic in a population, based on a random sample. Option A fits this description, while options B and C involve very small samples, which may not be representative of the entire population.

Question 5

For Questions , use the following narrative
Narrative: Test scores
Suppose that test scores on a particular exam have a mean of 77 and standard deviation of 5, and that they have a bell-shaped curve.
-{Test scores narrative} Suppose that the test scores are not bell-shaped, but are skewed to the right.You want to take a random sample and estimate the average test scored for this population.You want to be able to use the rule of sample means to interpret your results in this case.Under what (if any) conditions is this possible?

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Question 6

Explain, in words that a non-statistics student would understand, why the standard deviation of the various sample means taken from a population is smaller than the standard deviation of the individuals in the population? (In the first situation, assume all samples are of the same size, and that size is large.)

Accepted Answer

The answer of Explain, in words that a non-statistics student...

Question 7

For Questions , use the following narrative
Narrative: Test scores
Suppose that test scores on a particular exam have a mean of 77 and standard deviation of 5, and that they have a bell-shaped curve.
-{Test scores narrative} Suppose you randomly select a sample of size 100 from this population.Where would you expect their average test score to fall? Compare your answer to what you would expect from a single individual selected at random from this population.

Accepted Answer

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Narrative:...

Question 8

The standard deviation of the proportions from numerous random samples of size 1,000 from a population will be __________ the standard deviation of the proportions from numerous random samples of size 10,000 from the same population.

Accepted Answer

The answer of The standard deviation of the proportions from...

Question 9

For Questions , use the following narrative
Narrative: Test scores
Suppose that test scores on a particular exam have a mean of 77 and standard deviation of 5, and that they have a bell-shaped curve.
-{Test scores narrative} Suppose you take a single random sample of size 100 from this population, and you get a mean test score of 79.Is this something that you would have expected? Use a probability to justify your answer.

Accepted Answer

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Narrative:...

Question 10

If numerous large random samples or repetitions of the same size are taken from a population, the frequency curve made from proportions from the various samples will have an approximate __________ shape.

Accepted Answer

The answer of If numerous large random samples or repetitions...

Question 11

Which of the following are examples where you would be interested in estimating the population mean?

Accepted Answer

Estimating the population mean is relevant for quantitative data, such as the average lifespan of left-handed people. The other options involve categorical data or specific counts, not averages.

Question 12

If numerous large random samples or repetitions of the same size are taken from a population, the proportions from the various samples will have what approximate mean?

Accepted Answer

If numerous large random samples or repetitions of the same size are taken from a population, the proportions from the various samples will have an approximate mean of the true population proportion. This is known as the Law of Large Numbers, which states that as the sample size increases, the sample mean approaches the true population mean.

Question 13

For Questions , use the following narrative
Narrative: Test scores
Suppose that test scores on a particular exam have a mean of 77 and standard deviation of 5, and that they have a bell-shaped curve.
-{Test scores narrative} Suppose you take numerous random samples of size 100 from this population.Describe the shape and give the mean and standard deviation of the resulting frequency curve.

Accepted Answer

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Narrative:...

Question 14

In which of the following situations does the rule for sample means not apply?

Accepted Answer

The rule for sample means may not apply in situation C because the sample size is small (n=20) and salaries are often not normally distributed, potentially skewing the results.

Question 15

For Questions , use the following narrative
Narrative: Test scores
Suppose that test scores on a particular exam have a mean of 77 and standard deviation of 5, and that they have a bell-shaped curve.
-{Test scores narrative} Find and compare the answers to the following two questions; explain why your answers are the same or different.1) One individual is selected at random from the population.What range of test scores is reasonable to expect for this person? 2) A sample of 100 individuals is selected at random from the population.What range of average test scores is reasonable to expect for this group?

Accepted Answer

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Narrative:...

Question 16

For Questions , use the following narrative
Narrative: Test scores
Suppose that test scores on a particular exam have a mean of 77 and standard deviation of 5, and that they have a bell-shaped curve.
-{Test scores narrative} Suppose you take a single random sample of size 100 from this population, and you get a mean test score of 76.Is this something that you would have expected? Use a probability to justify your answer.

Accepted Answer

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

Question 17

If numerous large random samples or repetitions of the same size are taken from a population, the frequency curve made from proportions from the various samples will have what approximate shape?

Accepted Answer

According to the central limit theorem, the frequency curve made from proportions from numerous large random samples taken from a population will have a bell-shaped curve, regardless of the shape of the population itself. This is because the means from these samples will follow a normal distribution.

Question 18

{Politics narrative} Suppose numerous random samples of size 1,000 are taken from this population.The proportions of Republicans from the various samples of size 1,000 will have what approximate standard deviation?

Accepted Answer

The standard deviation of a proportion can be calculated as the square root of (p * (1-p) / n), where p is the proportion of Republicans in the population and n is the sample size. Assuming a 50-50 split between Republicans and Democrats, p = 0.5. Plugging in n=1000 and p=0.5, we get a standard deviation of sqrt(0.5 * 0.5 / 1000) = 0.015 or 1.5%. Therefore, the best choice is C.

Question 19

{Politics narrative} Suppose numerous random samples of size 1,000 are taken from this population.The proportions of Democrats from the various samples of size 1,000 will have what approximate standard deviation?

Accepted Answer

The standard deviation of sample proportions can be calculated using the formula sqrt(p(1-p)/n), where p is the population proportion (unknown in this case) and n is the sample size. Since we do not know the population proportion, we can use 0.5 as a conservative estimate to get an upper bound on the standard deviation. Therefore, sqrt(0.5*0.5/1000) = 0.015 or 1.5%.

Question 20

If numerous large random samples or repetitions of the same size are taken from a population, the frequency curve made from proportions from the various samples will have a mean that is __________ the true population proportion.

Accepted Answer

The answer of If numerous large random samples or repetitions...

Quiz 19: The Diversity of Samples From the Same Population

If numerous large random samples or repetitions of the same size are taken from a population, the frequency curve made from means from the various samples will have what approximate shape?

In which of the following situations does the rule for sample proportions apply?

The standard deviation of the proportions from numerous random samples of size 1,000 from a population will be __________ the standard deviation of the proportions from numerous random samples of size 10,000 from the same population.

If numerous large random samples or repetitions of the same size are taken from a population, the frequency curve made from proportions from the various samples will have an approximate __________ shape.

Which of the following are examples where you would be interested in estimating the population mean?

If numerous large random samples or repetitions of the same size are taken from a population, the proportions from the various samples will have what approximate mean?

In which of the following situations does the rule for sample means not apply?

If numerous large random samples or repetitions of the same size are taken from a population, the frequency curve made from proportions from the various samples will have what approximate shape?

{Politics narrative} Suppose numerous random samples of size 1,000 are taken from this population.The proportions of Republicans from the various samples of size 1,000 will have what approximate standard deviation?

{Politics narrative} Suppose numerous random samples of size 1,000 are taken from this population.The proportions of Democrats from the various samples of size 1,000 will have what approximate standard deviation?

If numerous large random samples or repetitions of the same size are taken from a population, the frequency curve made from proportions from the various samples will have a mean that is __________ the true population proportion.