Question 1

The owner of a fish market has an assistant who has determined that the weights of catfish are
Normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound.If a sample of
16 fish is taken, what would the standard error of the mean weight equal?

Accepted Answer

The standard error of the mean is calculated by dividing the standard deviation by the square root of the sample size: 0.8 / √16 = 0.2.

Question 2

The owner of a fish market has an assistant who has determined that the weights of catfish are
Normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound.If a sample of
64 fish yields a mean of 3.4 pounds, what is probability of obtaining a sample mean this large or
Larger?

Accepted Answer

The answer of The owner of a fish market has...

Question 3

The owner of a fish market has an assistant who has determined that the weights of catfish are
Normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound.What
Percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds?

Accepted Answer

The answer of The owner of a fish market has...

Question 4

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

Accepted Answer

As the sample size increases, the influence of an extreme value is diluted because it is averaged out over a larger number of observations, reducing its impact on the sample mean.

Question 5

True or False: 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

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal if the sample size is sufficiently large, typically n ≥ 30, regardless of the population distribution shape.

Question 6

True or False: If the population distribution is unknown, 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

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal if the sample size is sufficiently large, typically n ≥ 30, regardless of the population distribution.

Question 7

True or False: If the population distribution is symmetric, the sampling distribution of the mean
can be approximated by the normal distribution if the samples contain 15 observations.

Accepted Answer

If the population distribution is symmetric, the sampling distribution of the mean can be approximated by the normal distribution with a relatively small sample size, such as 15, due to the Central Limit Theorem.

Question 8

True or False: 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 4 cars is selected, there is approximately a 68.26% chance that the sample mean will be
between 13 and 17 gallons.

Accepted Answer

The answer of True or False: If the amount of...

Question 9

The standard error of the population proportion will become larger

Accepted Answer

The standard error of the population proportion is largest when the population proportion is at 0.50 because the formula for the standard error of a proportion includes the term sqrt[p(1-p)/n], where p is the population proportion and n is the sample size. The product p(1-p) reaches its maximum value at p = 0.5, making the standard error largest at this point.

Question 10

For sample size 1, the sampling distribution of the mean will be normally distributed

Accepted Answer

For sample size 1, the sampling distribution of the mean will be normally distributed only if the population from which the sample is drawn is normally distributed.

Question 11

The owner of a fish market has an assistant who has determined that the weights of catfish are
Normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound.If a sample of
25 fish yields a mean of 3.6 pounds, what is the Z-score for this observation?

Accepted Answer

The answer of The owner of a fish market has...

Question 12

True or False: A sampling distribution is a distribution for a statistic.

Accepted Answer

A sampling distribution is the probability distribution of a given statistic based on a random sample, and it shows how the statistic varies from sample to sample.

Question 13

True or False: 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

The Central Limit Theorem states that for large sample sizes, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution. In this case, the sample size is 16, which is large enough to apply the Central Limit Theorem. Therefore, the sampling distribution of the sample mean will be approximately normal with a mean of 15 gallons and a standard deviation of 4/sqrt(16) = 1 gallon. Using the standard normal distribution, we can find that the probability of a sample mean between 14 and 16 gallons is approximately 68.26%.

Question 14

The standard error of the mean for a sample of 100 is 30.In order to cut the standard error of the
Mean to 15, we would

Accepted Answer

The standard error of the mean is inversely proportional to the square root of the sample size. To halve the standard error from 30 to 15, the sample size must be quadrupled from 100 to 400.

Question 15

For sample sizes greater than 30, the sampling distribution of the mean will be approximately
Normally distributed

Accepted Answer

According to the Central Limit Theorem, for sample sizes greater than 30, the sampling distribution of the mean will be approximately normally distributed regardless of the shape of the population.

Question 16

For sample size 16, the sampling distribution of the mean will be approximately normally
Distributed

Accepted Answer

The Central Limit Theorem states that the sampling distribution of the mean will be approximately normal if the sample size is large enough or if the population distribution is symmetrical. With a sample size of 16, the population should be symmetrical for the sampling distribution to be approximately normal.

Question 17

True or False: 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, then 99.73% of
all cars will purchase between 3 and 27 gallons.

Accepted Answer

The answer of True or False: If the amount of...

Question 18

True or False: As the sample size increases, the standard error of the mean increases.

Accepted Answer

The standard error of the mean decreases as the sample size increases because it is inversely proportional to the square root of the sample size.

Question 19

Which of the following is true regarding the sampling distribution of the mean for a large sample
Size?

Accepted Answer

According to the Central Limit Theorem, the sampling distribution of the mean will be approximately normal for a large sample size, with the same mean as the population but a smaller standard deviation, specifically the population standard deviation divided by the square root of the sample size.

Question 20

True or False: 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

According to the Central Limit Theorem, the sampling distribution of the sample mean will be approximately normal with a mean of 15 gallons and a standard deviation of 0.5 gallons (4/√64). Using the empirical rule (68-95-99.7 rule), about 95.44% of the sample means will fall within two standard deviations (1 gallon) of the mean, i.e., between 14 and 16 gallons.

Quiz 7: Sampling Distributions

The owner of a fish market has an assistant who has determined that the weights of catfish are Normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound.If a sample of 16 fish is taken, what would the standard error of the mean weight equal?

The owner of a fish market has an assistant who has determined that the weights of catfish are Normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound.If a sample of 64 fish yields a mean of 3.4 pounds, what is probability of obtaining a sample mean this large or Larger?

The owner of a fish market has an assistant who has determined that the weights of catfish are Normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound.What Percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds?

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

True or False: 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.

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

True or False: If the population distribution is symmetric, the sampling distribution of the mean can be approximated by the normal distribution if the samples contain 15 observations.

The standard error of the population proportion will become larger

For sample size 1, the sampling distribution of the mean will be normally distributed

The owner of a fish market has an assistant who has determined that the weights of catfish are Normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound.If a sample of 25 fish yields a mean of 3.6 pounds, what is the Z-score for this observation?

True or False: A sampling distribution is a distribution for a statistic.

The standard error of the mean for a sample of 100 is 30.In order to cut the standard error of the Mean to 15, we would

For sample sizes greater than 30, the sampling distribution of the mean will be approximately Normally distributed

For sample size 16, the sampling distribution of the mean will be approximately normally Distributed

True or False: 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, then 99.73% of all cars will purchase between 3 and 27 gallons.

True or False: As the sample size increases, the standard error of the mean increases.

Which of the following is true regarding the sampling distribution of the mean for a large sample Size?