Deck 7: Sampling Distributions

Question 1

If the amount of petrol purchased per car at a large petrol station has a population mean of $15 and a population standard deviation of $4 and it is assumed that the amount of petrol 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.

Answer 1

True

Question 2

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.

Answer 2

True

Question 3

The sampling distribution of a sample statistic represents what would result if all possible samples from a population were drawn.

Answer 3

True

Question 4

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.

Question 5

As the sample size increases,the standard error of the mean increases.

Question 6

One key requirement of sampling in inferential statistics is that

A)the sample size must be proportional to the population size.
B)the members of the sample must be selected systematically.
C)the sample size must be determined in advance.
D)the sample must include representation of all major groups within the population.

Question 7

The amount of time it takes to complete an examination has a skewed-left distribution with a mean of 65 minutes and a standard deviation of 8 minutes.If 64 students were randomly sampled,the probability that the sample mean of the sampled students exceeds 71 minutes is approximately 0.

Question 8

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

Question 9

If the amount of petrol purchased per car at a large petrol station has a population mean of $15 and a population standard deviation of $4 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.

Question 10

If the amount of petrol purchased per car at a large petrol station has a population mean of $15 and a population standard deviation of $4,then 99.73% of all cars will purchase between $3 and $27.

Question 11

A sampling distribution is a probability distribution for a statistic.

Question 12

The Central Limit Theorem is considered powerful in statistics because it works for any population distribution provided the sample size is sufficiently large and the population mean and standard deviation are known.

Question 13

If the population distribution is symmetric,the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 15 observations.

Question 14

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

Question 15

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.

Question 16

If the amount of petrol purchased per car at a large petrol station has a population mean of $15 and a population standard deviation of $4 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.

Question 17

In inferential statistics,the sampling distribution of the sample mean represents ________.

Question 18

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.

Question 19

A statistic calculated from a sample is used to estimate the corresponding

A)sample.
B)parameter.
C)distribution.
D)statistic.

Question 20

Suppose μ = 50 and σ² = 100 for a population.In a sample where n = 100 is randomly taken,90% of all possible sample means will fall between 49 and 51.

Question 21

Sampling error can be completely eliminated by taking larger sample sizes.

Question 22

The sample mean is an unbiased estimate of the population mean.

Question 23

A sample of size 25 provides a sample variance of 400.The standard error,in this case equal to 4,is best described as the estimate of the standard deviation of means calculated from samples of size 25.

Question 24

The amount of bleach a machine pours into bottles has a mean of 1080 grams with a standard deviation of 4.5 grams.Suppose we take a random sample of 36 bottles filled by this machine.The sampling distribution of the sample mean has a standard error of 4.5.

Question 25

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.

Question 26

If the expectation of a sampling distribution is located at the parameter it is estimating,then we call that sampling distribution

A)minimum variance.
B)biased.
C)random.
D)unbiased.

Question 27

Sampling distributions describe the probability distribution of

A)sample statistics.
B)population parameters.
C)Both parameters and statistics.
D)Neither parameters nor statistics.

Question 28

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

Question 29

The Central Limit Theorem is important in statistics because

A)for any sized sample,it says the sampling distribution of the sample mean is approximately normal.
B)for any population,it says the sampling distribution of the sample mean is approximately normal,regardless of the sample size.
C)for a large n,it says the population is approximately normal.
D)for a large n,it says the sampling distribution of the sample mean is approximately normal,regardless of the shape of the population.

Question 30

The standard error of the mean

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

Question 31

The sample proportion is an unbiased estimate of the population proportion.

Question 32

In inferential statistics,the standard error of the sample mean assesses the uncertainty or error of estimation.

Question 33

The amount of bleach a machine pours into bottles has a mean of 1080 grams with a standard deviation of 4.5 grams.Suppose we take a random sample of 36 bottles filled by this machine.The sampling distribution of the sample mean has a mean of 1080.

Question 34

The amount of bleach a machine pours into bottles has a mean of 1080 grams with a standard deviation of 4.5 grams.Suppose we take a random sample of 36 bottles filled by this machine.The sampling distribution of the sample mean will be approximately normal only if the population sampled is normal.

Question 35

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

Question 36

Sampling error can be reduced by taking larger sample sizes.

Question 37

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

Question 38

An unbiased estimator will have a value,on average across samples,equal to the population parameter value.

Question 39

For air travellers,one of the biggest complaints is of the waiting time between when the aeroplane taxis away from the terminal until the flight takes off.This waiting time is known to have a skewed-right distribution with a mean of 10 minutes and a standard deviation of 8 minutes.Suppose 100 flights have been randomly sampled.Describe the sampling distribution of the mean waiting time between when the aeroplane taxis away from the terminal until the flight takes off for these 100 flights.

A)Distribution is approximately normal with mean = 10 minutes and standard error = 8 minutes.
B)Distribution is skewed-right with mean = 10 minutes and standard error = 8 minutes.
C)Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes.
D)Distribution is skewed-right with mean = 10 minutes and standard error = 0.8 minutes.

Question 40

Which of the following statements about the sampling distribution of the sample mean is incorrect?

A)The standard deviation of the sampling distribution of the sample mean is equal to σ.
B)The sampling distribution of the sample mean is generated by repeatedly taking samples of size n and computing the sample means.
C)The mean of the sampling distribution of the sample mean is equal to μ.
D)The sampling distribution of the sample mean is approximately normal whenever the sample size is sufficiently large (n ≥ 30).

Question 41

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

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 population when n is large.
C)It allows us to disregard the shape of the sampling distribution when the size of the population is large.
D)It allows us to disregard the size of the population we are sampling from.

Question 42

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

A)if the sample is normally distributed.
B)if the shape of the population is symmetrical.
C)if the sample standard deviation is known.
D)regardless of the shape of the population.

Question 43

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

A)1.875
B)18.750
C)2.500
D)0.750

Question 44

Suppose the ages of students in first-year Statistics follow a skewed-right distribution with a mean of 23 years and a standard deviation of 3 years.If we randomly sampled 100 students,which of the following statements about the sampling distribution of the sample mean age is incorrect?

A)The mean of the sampling distribution is equal to 23 years.
B)The standard error of the sampling distribution is equal to 0.3 years.
C)The shape of the sampling distribution is approximately normal.
D)The standard deviation of the sampling distribution is equal to 3 years.

Question 45

Australian football salaries averaged $150,000 with a standard deviation of $80,000 in a recent year.Suppose a sample of 100 football players was taken.What was the standard error for the sample mean salary?

A)$8,000
B)$800,000
C)$8 million
D)$150,000

Question 46

Suppose a sample of n = 50 items is drawn from a population of manufactured products and the weight,X,of each item is recorded.Prior experience has shown that the weight has a probability distribution with μ = 180 grams and σ = 75 grams.Which of the following is true about the sampling distribution of the sample mean if a sample size of 15 is selected?

A)The shape of the sample distribution is approximately normal.
B)The standard deviation of the sampling distribution is 75 grams.
C)The mean of the sampling distribution is 180 grams.
D)All of the above are correct.

Question 47

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

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

Question 48

The owner of a fish market has an assistant who has determined that the weights of rainbow trout are normally distributed,with mean of 3.2 kilograms and standard deviation of 0.8 kilogram.If a sample of 64 fish yields a mean of 3.4 kilograms,what is the probability of obtaining a sample mean this large or larger?

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

Question 49

The standard error of the mean for a sample of 100 is 30.What is the standard deviation?

A)400
B)25
C)300
D)200

Question 50

The amount of bleach a machine pours into bottles has a mean of 1080 grams with a standard deviation of 4.5 grams.Suppose we take a random sample of 36 bottles filled by this machine.The probability that the mean of the sample exceeds 1080.3 grams is ________.

Question 51

At a computer manufacturing company,the actual size of computer chips is normally distributed with a mean of 1 cm and a standard deviation of 0.1 cm.A random sample of 12 computer chips is taken.What is the standard error for the sample mean?

A)0.029
B)0.120
C)0.091
D)0.050

Question 52

A sample that does not provide a good representation of the population from which it was collected is referred to as a(n)________ sample.

Question 53

Sales prices of matchbox cars from the 1960s are known to possess a skewed-right distribution with a mean sale price of $5.25 and a standard deviation of $2.80.Suppose a random sample of 100 cars from the 1960s is selected.Describe the sampling distribution for the sample mean sale price of the selected cars.

A)Skewed-right with a mean of $5.25 and a standard error of $2.80.
B)Normal with a mean of $5.25 and a standard error of $2.80.
C)Normal with a mean of $5.25 and a standard error of $0.28.
D)Skewed-right with a mean of $5.25 and a standard error of $0.28.

Question 54

Suppose the ages of students in first-year Statistics 101 follow a skewed-right distribution with a mean of 23 years and a standard deviation of 3 years.If we randomly sampled 100 students,which of the following is true about the sampling distribution of the sample mean?

A)The shape of the sampling distribution is approximately normal.
B)The mean of the sampling distribution is equal to 23 years.
C)The standard deviation of the sampling distribution is equal to 3 years.
D)The standard error of the sampling distribution is equal to 0.3 years.

Question 55

Australian football salaries averaged $150,000 with a standard deviation of $80,000 in a recent year.Suppose a sample of 100 football players was taken.Find the approximate probability that the average salary of the 100 players exceeded $100,000.

A)Approximately 1
B)0.2357
C)0.7357
D)Approximately 0

Question 56

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

A)only if the shape of the population is symmetrical.
B)regardless of the shape of the population.
C)only if the population values are positive.
D)only if the population is normally distributed.

Question 57

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

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

Question 58

The owner of a fish market has an assistant who has determined that the weights of rainbow trout are normally distributed,with mean of 3.2 kilograms and standard deviation of 0.8 kilogram.What percentage of samples of 4 fish will have sample means between 3.0 and 4.0 kilograms?

A)67%
B)29%
C)84%
D)16%

Question 59

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

A)0.200
B)0.800
C)0.003
D)0.050

Question 60

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

A)regardless of the shape of the population.
B)only if the population is normally distributed.
C)only if the shape of the population is symmetrical.
D)only if the standard deviation of the samples are known.

Question 61

At a computer manufacturing company,the actual size of computer chips is normally distributed with a mean of 1 cm and a standard deviation of 0.1 cm.A random sample of 12 computer chips is taken.What is the probability that the sample mean will be between 0.99 and 1.01 cm?

Question 62

A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes.Suppose a random sample of 64 purchasers of this table saw is taken.So,95% of the sample means based on samples of size 64 will be between ________ and ________.

Question 63

The amount of pyridoxine (in grams)per multiple vitamin is normally distributed with μ = 110 grams and σ = 25 grams.A sample of 25 vitamins is to be selected.What is the probability that the sample mean will be less than 100 grams?

Question 64

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

Question 65

The amount of pyridoxine (in grams)per multiple vitamin is normally distributed with μ = 110 grams and σ= 25 grams.A sample of 25 vitamins is to be selected.So,the middle 70% of all sample means will fall between what two values?

Question 66

The amount of bleach a machine pours into bottles has a mean of 1080 grams with a standard deviation of 4.5 grams.Suppose we take a random sample of 36 bottles filled by this machine.So,95% of the sample means based on samples of size 36 will be between ________ and ________.

Question 67

The amount of pyridoxine (in grams)per multiple vitamin is normally distributed with μ = 110 grams and σ = 25 grams.A sample of 25 vitamins is to be selected.What is the probability that the sample mean will be between 100 and 120 grams?

Question 68

The distribution of the number of loaves of bread sold per day by a large bakery over the past 5 years has a mean of 7,750 and a standard deviation of 145 loaves.Suppose a random sample of n = 40 days has been selected.What is the approximate probability that the average number of loaves sold in the sampled days exceeds 7,895 loaves?

Question 69

A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes.Suppose a random sample of 64 purchasers of this table saw is taken.The probability that the sample mean will be between 77 and 89 minutes is ________.

Question 70

A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes.Suppose a random sample of 64 purchasers of this table saw is taken.The standard deviation of the sampling distribution of the sample mean is ________ minutes.

Question 71

The amount of pyridoxine (in grams)per multiple vitamin is normally distributed with μ = 110 grams and σ= 25 grams.A sample of 25 vitamins is to be selected.So,95% of all sample means will be greater than how many grams?

Question 72

At a computer manufacturing company,the actual size of computer chips is normally distributed with a mean of 1 cm and a standard deviation of 0.1 cm.A random sample of 12 computer chips is taken.What is the probability that the sample mean will be below 0.95 cm?

Question 73

A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes.Suppose a random sample of 64 purchasers of this table saw is taken.The probability that the sample mean will be greater than 88 minutes is ________.

Question 74

The amount of pyridoxine (in grams)per multiple vitamin is normally distributed with μ = 110 grams and σ = 25 grams.A sample of 25 vitamins is to be selected.What is the probability that the sample mean will be greater than 100 grams?

Question 75

The amount of bleach a machine pours into bottles has a mean of 1080 grams with a standard deviation of 4.5 grams.Suppose we take a random sample of 36 bottles filled by this machine.The probability that the mean of the sample is less than 1080.9 is ________.

Question 76

A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes.Suppose a random sample of 64 purchasers of this table saw is taken.The probability that the sample mean will be less than 82 minutes is ________.

Question 77

The amount of bleach a machine pours into bottles has a mean of 1080 grams with a standard deviation of 4.5 grams.Suppose we take a random sample of 36 bottles filled by this machine.The probability that the mean of the sample is between 1018.9 and 1022.3 grams is ________.

Question 78

At a computer manufacturing company,the actual size of computer chips is normally distributed with a mean of 1 cm and a standard deviation of 0.1 cm.A random sample of 12 computer chips is taken.Above what value do 2.5% of the sample means fall?

Question 79

The amount of bleach a machine pours into bottles has a mean of 1080 grams with a standard deviation of 4.5 grams.Suppose we take a random sample of 36 bottles filled by this machine.The probability that the mean of the sample is between 1078.2 and 1079.4 grams is ________.

Question 80

A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes.Suppose a random sample of 64 purchasers of this table saw is taken.The mean of the sampling distribution of the sample mean is ________ minutes.