Question 1

μ The am = 110 gramount of tea leaves in a can froms and σ = 25 grams. A sam a particular production line is normple of 25 cans is to be selected. What is the probabilityally distributed with
that the sample mean will be between 100 and 120 grams?

Accepted Answer

The answer of μ The am = 110 gramount of...

Question 2

The amount of time required for an oil and filter change on an automobile is normally
distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample
of 16 cars is selected. What is the standard error of the mean?

Accepted Answer

The answer of The amount of time required for an...

Question 3

A sampling distribution is a distribution for a statistic.

Accepted Answer

A sampling distribution is a distribution that shows the possible values of a statistic based on all possible samples that could be taken from a population.

Question 4

μThe am = 110 gramount of tea leaves in a can froms and σ = 25 grams. A sam a particular production line is normple of 25 cans is to be selected. So, the mally distributed with iddle 70% of
all sample means will fall between what two values?

Accepted Answer

The answer of μThe am = 110 gramount of tea...

Question 5

μThe am = 110 gramount of tea leaves in a can froms and σ = 25 grams. A sam a particular production line is normple of 25 cans is to be selected. What is the probabilityally distributed with
that the sample mean will be greater than 100 grams?

Accepted Answer

The answer of μThe am = 110 gramount of tea...

Question 6

If the population distribution is skewed, in most cases the sampling distribution
of the mean can be approximated by the normal distribution if the samples contain at least 30
observations.

Accepted Answer

This statement is true. According to the Central Limit Theorem, the sampling distribution of the mean approaches a normal distribution as sample size increases, even if the population distribution is skewed. A sample size of at least 30 is typically considered sufficient for this approximation to hold.

Question 7

For distributions such as the normal distribution, the arithmetic mean is
considered more stable from sample to sample than other measures of central tendency.

Accepted Answer

The arithmetic mean of a normal distribution is a very stable measure of central tendency because it represents the center of the distribution and is less influenced by extreme values compared to other measures like the median or mode. Therefore, the answer is true.

Question 8

Suppose μ = 80 and σ = 20 for a population. In a sample where n = 100 is
randomly taken, 95% of all possible sample means will fall above 76.71.

Accepted Answer

This statement is true according to the central limit theorem, which states that as sample size increases, the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. Therefore, with a sample size of 100, the standard error would be σ/√n = 20/√100 = 2. Thus, a sample mean of 76.71 (which is 1.645 standard errors below the population mean) would be within the 5% of sample means that fall below the population mean minus 1.645 standard errors, which is equal to 80 - 1.645(2) = 76.71. Therefore, 95% of all possible sample means would fall above 76.71.

Question 9

The standard error of the mean is also known as the standard deviation of the
sampling distribution of the sample mean.

Accepted Answer

The standard error of the mean is the standard deviation of the sampling distribution of the sample mean.

Question 10

μThe am = 110 gramount of tea leaves in a can froms and σ = 25 grams. A sam a particular production line is normple of 25 cans is to be selected. So, 95% of all samally distributed with ple
means will be greater than how many grams?

Accepted Answer

The answer of μThe am = 110 gramount of tea...

Question 11

The Central Limit Theorem ensures that the sampling distribution of the sample
mean approaches a normal distribution as the sample size increases.

Accepted Answer

The Central Limit Theorem states that as sample size increases, the sampling distribution of the sample mean approaches a normal distribution regardless of the underlying population distribution.

Question 12

If the amount of gasoline purchased per car at a large service station has a
population mean of 15 gallons and a population standard deviation of 4 gallons and it is assumed
that the amount of gasoline purchased per car is symmetric, there is approximately a 68.26%
chance that a random sample of 16 cars will have a sample mean between 14 and 16 gallons.

Accepted Answer

From the Central Limit Theorem, we know that the distribution of sample means will be approximately normal with a mean of the population mean and a standard deviation of the population standard deviation divided by the square root of the sample size (4/sqrt(16) = 1). Thus, a sample mean between 14 and 16 gallons is within one standard deviation of the population mean of 15 gallons. By the empirical rule, there is approximately a 68.26% chance that a random sample of 16 cars will fall within one standard deviation of the population mean. Therefore, the statement is true.

Question 13

As the size of the sample is increased, the standard deviation of the sampling
distribution of the sample mean for a normally distributed population will stay the same.

Accepted Answer

As the size of the sample is increased, the standard deviation of the sampling distribution of the sample mean, also known as the standard error, decreases. This is because the standard error is inversely related to the square root of the sample size.

Question 14

μThe am = 110 gramount of tea leaves in a can froms and σ = 25 grams. A sam a particular production line is normple of 25 cans is to be selected. What is the ally distributed with
probability that the sample mean will be less than 100 grams?

Accepted Answer

The answer of μThe am = 110 gramount of tea...

Question 15

If the amount of gasoline purchased per car at a large service station has a
population mean of 15 gallons and a population standard deviation of 4 gallons and a random
sample of 64 cars is selected, there is approximately a 95.44% chance that the sample mean will
be between 14 and 16 gallons.

Accepted Answer

This is true because we can use the central limit theorem to approximate the distribution of sample means to be normal with a mean of 15 and standard deviation of (4/√64) = 0.5. Then, we can find the z-scores corresponding to 14 and 16 using the formula z = (x̄ - μ) / (σ / √n), where x̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. The z-score for 14 is z = (14 - 15) / 0.5 = -2, and the z-score for 16 is z = (16 - 15) / 0.5 = 2. Then, using a standard normal table or calculator, we can find that the area between -2 and 2 is approximately 0.9544, which represents the probability that the sample mean falls between 14 and 16 gallons.

Question 16

Suppose μ = 50 and σ = 10 for a population. In a sample where n = 100 is
randomly taken, 90% of all possible sample means will fall between 49 and 51.

Accepted Answer

The answer of Suppose μ = 50 and σ =...

Question 17

Suppose μ = 50 and σ = 10 for a population. In a sample where n = 100 is
randomly taken, 95% of all possible sample means will fall between 48.04 and 51.96.

Accepted Answer

This statement is a correct interpretation of the 95% confidence interval for the sample mean given the population mean and standard deviation.

Question 18

A sampling distribution is defined as the probability distribution of possible
sample sizes that can be observed from a given population.

Accepted Answer

A sampling distribution is the probability distribution of possible sample statistics, such as means or proportions, that can be observed from a given population. The distribution of sample sizes is not the same as the sampling distribution.

Question 19

The fact that the sample means are less variable than the population data can be
observed from the standard error of the mean.

Accepted Answer

The standard error of the mean measures the variability or precision of the sample mean, and this value is generally smaller than the variability of the population data. Therefore, the statement is true.

Question 20

As the sample size increases, the effect of an extreme value on the sample mean
becomes smaller.

Accepted Answer

This is true because as the sample size increases, the impact of any single data point on the overall mean decreases. This is due to the central limit theorem, which states that as the sample size increases, the distribution of sample means approaches a normal distribution, making extreme values less influential.

Quiz 7: Sampling Distributions

μ The am = 110 gramount of tea leaves in a can froms and σ = 25 grams. A sam a particular production line is normple of 25 cans is to be selected. What is the probabilityally distributed with that the sample mean will be between 100 and 120 grams?

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What is the standard error of the mean?

A sampling distribution is a distribution for a statistic.

μThe am = 110 gramount of tea leaves in a can froms and σ = 25 grams. A sam a particular production line is normple of 25 cans is to be selected. So, the mally distributed with iddle 70% of all sample means will fall between what two values?

μThe am = 110 gramount of tea leaves in a can froms and σ = 25 grams. A sam a particular production line is normple of 25 cans is to be selected. What is the probabilityally distributed with that the sample mean will be greater than 100 grams?

If the population distribution is skewed, in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 30 observations.

For distributions such as the normal distribution, the arithmetic mean is considered more stable from sample to sample than other measures of central tendency.

Suppose μ = 80 and σ = 20 for a population. In a sample where n = 100 is randomly taken, 95% of all possible sample means will fall above 76.71.

The standard error of the mean is also known as the standard deviation of the sampling distribution of the sample mean.

μThe am = 110 gramount of tea leaves in a can froms and σ = 25 grams. A sam a particular production line is normple of 25 cans is to be selected. So, 95% of all samally distributed with ple means will be greater than how many grams?

The Central Limit Theorem ensures that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases.

As the size of the sample is increased, the standard deviation of the sampling distribution of the sample mean for a normally distributed population will stay the same.

μThe am = 110 gramount of tea leaves in a can froms and σ = 25 grams. A sam a particular production line is normple of 25 cans is to be selected. What is the ally distributed with probability that the sample mean will be less than 100 grams?

If the amount of gasoline purchased per car at a large service station has a population mean of 15 gallons and a population standard deviation of 4 gallons and a random sample of 64 cars is selected, there is approximately a 95.44% chance that the sample mean will be between 14 and 16 gallons.

Suppose μ = 50 and σ = 10 for a population. In a sample where n = 100 is randomly taken, 90% of all possible sample means will fall between 49 and 51.

Suppose μ = 50 and σ = 10 for a population. In a sample where n = 100 is randomly taken, 95% of all possible sample means will fall between 48.04 and 51.96.

A sampling distribution is defined as the probability distribution of possible sample sizes that can be observed from a given population.

The fact that the sample means are less variable than the population data can be observed from the standard error of the mean.

As the sample size increases, the effect of an extreme value on the sample mean becomes smaller.