Question 1

Which of the following is true about the sampling distribution of the sample mean?

Accepted Answer

A) The mean of the sampling distribution is always μ. 
B) The standard deviation of the sampling distribution is always σ. 
C) The shape of the sampling distribution is always approximately normal. 
D) All the above are true.

Question 2

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

A) True 
 B)False

Question 3

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

Accepted Answer

A) True 
 B)False

Question 4

Why is the Central Limit Theorem so important to the study of sampling distributions?

Accepted Answer

A) It allows us to disregard the size of the sample selected when the population is not normal. 
B) It allows us to disregard the shape of the sampling distribution when the size of the population is large. 
C) It allows us to disregard the size of the population we are sampling from. 
D) It allows us to disregard the shape of the population when n is large.

Question 5

The amount of tea leaves in a can from a production line is normally distributed with μ = 110 grams and σ = 25 grams.A sample of 25 cans is to be selected.So,the middle 70% of all sample means will fall between what two values?

Accepted Answer

The answer of The amount of tea leaves in a...

Question 6

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 7

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

A) 0.0001 
B) 0.0013 
C) 0.0228 
D) 0.4987

Question 8

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past.Suppose a sample of 100 major league players was taken.What was the standard error for the sample mean salary?

Accepted Answer

A) $0.012 million 
B) $0.12 million 
C) $12 million 
D) $1,200.0 million

Question 9

The standard error of the mean

Accepted Answer

A) is never larger than the standard deviation of the population. 
B) decreases as the sample size increases. 
C) measures the variability of the mean from sample to sample. 
D) All the above.

Question 10

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

A) True 
 B)False

Question 11

SCENARIO 7-2
The mean selling price of new homes in a small town over a year was $115,000.The population standard deviation was $25,000.A random sample of 100 new home sales from this city was taken.
-Referring to Scenario 7-2,what is the probability that the sample mean selling price was between
$114,000 and $116,000?

Accepted Answer

The answer of SCENARIO 7-2
The mean selling price of new...

Question 12

SCENARIO 7-5
According to an article,19% of the entire population in a developing country has high-speed access to the Internet.Random samples of size 200 are selected from the country's population.
-Referring to Scenario 7-5,among all the random samples of size 200,90 % will have more than _____ % who have high-speed access to the Internet.

Accepted Answer

The answer of SCENARIO 7-5
According to an article,19% of the...

Question 13

SCENARIO 7-4
According to a survey,only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected.
-Referring to Scenario 7-4,90% of the samples will have more than what percentage of customers who will make a purchase after visiting the web site?

Accepted Answer

The answer of SCENARIO 7-4
According to a survey,only 15% of...

Question 14

SCENARIO 7-6
Online customer service is a key element to successful online retailing.According to a marketing survey,37.5% of online customers take advantage of the online customer service.Random samples of 200 customers are selected.
-Referring to Scenario 7-6,the population mean of all possible sample proportions is .

Accepted Answer

The answer of SCENARIO 7-6
Online customer service is a key...

Question 15

SCENARIO 7-4
According to a survey,only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected.
-Referring to Scenario 7-4,the mean of all the sample proportions of customers who will make a purchase after visiting the web site is .

Accepted Answer

The answer of SCENARIO 7-4
According to a survey,only 15% of...

Question 16

SCENARIO 7-5
According to an article,19% of the entire population in a developing country has high-speed access to the Internet.Random samples of size 200 are selected from the country's population.
-Referring to Scenario 7-5,the standard error of all the sample proportions is .

Accepted Answer

The answer of SCENARIO 7-5
According to an article,19% of the...

Question 17

The mean score of all pro golfers for a course has a mean of 70 and a standard deviation of 3.0.Suppose 36 pro golfers played the course today.Find the probability that the mean score of the 36 pro golfers exceeded 71.

Accepted Answer

The answer of The mean score of all pro golfers...

Question 18

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

Accepted Answer

A) True 
 B)False

Question 19

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

Accepted Answer

A) increase the sample size to 200. 
B) increase the sample size to 400. 
C) decrease the sample size to 50. 
D) decrease the sample to 25.

Question 20

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

Accepted Answer

A) It has the same shape,mean,and standard deviation as the population. 
B) It has a normal distribution with the same mean and standard deviation as the population. 
C) It has the same shape and mean as the population but has a smaller standard deviation. 
D) It has a normal distribution with the same mean as the population but with a smaller standard deviation.

Exam 7: Sampling Distributions

Which of the following is true about the sampling distribution of the sample mean?

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.

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

Why is the Central Limit Theorem so important to the study of sampling distributions?

The amount of tea leaves in a can from a production line is normally distributed with μ = 110 grams and σ = 25 grams.A sample of 25 cans is to be selected.So,the middle 70% of all sample means will fall between what two values?

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?

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?

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past.Suppose a sample of 100 major league players was taken.What was the standard error for the sample mean salary?

The standard error of the mean

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.

SCENARIO 7-4 According to a survey,only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected. -Referring to Scenario 7-4,the mean of all the sample proportions of customers who will make a purchase after visiting the web site is .

SCENARIO 7-5 According to an article,19% of the entire population in a developing country has high-speed access to the Internet.Random samples of size 200 are selected from the country's population. -Referring to Scenario 7-5,the standard error of all the sample proportions is .

The mean score of all pro golfers for a course has a mean of 70 and a standard deviation of 3.0.Suppose 36 pro golfers played the course today.Find the probability that the mean score of the 36 pro golfers exceeded 71.

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

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

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