Deck 7: Sampling Methods and the Central Limit Theorem

Question 1

i. An estimate of the population mean based on a large sample is less reliable than an estimate made using a small sample. ii. The standard error of the mean will vary according to the size of the sample that is in the denominator. As the sample size n gets larger, the variability of the sample means gets smaller.
iii. To determine the value of the standard error of the mean, the total error is divided by the sample size.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement, but not (ii) or (iii).
C) (ii) is a correct statement, but not (i) or (iii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Answer 1

(ii) is a correct statement, but not (i) or (iii).

Question 2

i. If the sample size keeps getting larger and larger and finally equals the size of the population, there would be no error in predicting the population mean because the sample size and the size of the population would be the same. ii. A simple random sample assumes that each item or person in the population has an equal chance of being included.
iii. We can expect some difference between sample statistics and the corresponding population parameters. This difference is called the sampling error.

A) (i), (ii), and (iii) are all correct statements
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Answer 2

(i), (ii), and (iii) are all correct statements

Question 3

i. It is often not feasible to study the entire population because it is impossible to check all the items in the population. ii. Sampling a population is often necessary because the cost of studying all the items in the population is prohibitive.
iii. Sampling is a sign of laziness on the part of the statistician.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Answer 3

(i) and (ii) are correct statements but not (iii).

Question 4

What is it called when all the items in a population have a chance of being selected in a sample?

A) Random sampling
B) z-score
C) Sampling error
D) Non probability sampling

Question 5

Suppose we select every fifth invoice in a file. What type of sampling is this?

A) Simple random
B) Stratified random
C) Cluster
D) Systematic

Question 6

Sampling error is the difference between a corresponding sample statistic and the

A) sample mean.
B) biased sample.
C) population parameter.
D) chance error.

Question 7

(i. As the sample size (n) increases, the spread in the distribution of the sample means stays the same. (ii) If the sampling size equals the population size, the sampling error is 1.
(iii) If a population is normally distributed, the sampling distribution of the mean is normally distributed.

A) (i), (ii), and (iii) are all correct statements.
B) (iii) is a correct statement, but not (i) or (ii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 8

Suppose we select every tenth invoice in a file. What type of sampling is this?

A) Random
B) Cluster
C) Stratified
D) Systematic

Question 9

The mean of all possible sample means is equal to the

A) population variance.
B) $\sigma$ ²/n.
C) sample variance.
D) population mean.

Question 10

Which of the following is the standard error of the mean?

A) µ
B) x/n
C)
D) s/ $\surd$ n

Question 11

We wish to study the advertising expenditures for the 200 largest companies in Canada. Suppose the objective of the study is to determine whether firms with high returns on equity (a measure of profitability) spent more of each sales dollar on advertising than firms with a low return or deficit. To make sure that the sample is a fair representation of the 200 companies, the companies are grouped on percent return on equity What is this type of sampling called?

A) Simple random
B) Stratified random
C) Cluster
D) Systematic

Question 12

i. If probability sampling is done, each item in the population has a chance of being chosen. ii. If the size of a sample equals the size of the population, we would not expect any error in estimating the population parameter.

A) (i) and (ii) are both correct statements.
B) (i) is correct but not (ii).
C) (ii) is correct but not (i).
D) (ii) and (ii) are both false statements.

Question 13

An experiment involves randomly selecting a sample of 256 middle managers for study. One item of interest is their mean annual income. The sample mean is computed to be $35,420 and the sample standard deviation is $2,050. What is the standard error of the mean?

A) $5.65
B) $128.13
C) $138.36
D) $2,050
E) $8.01

Question 14

What is the difference between a sample mean and the population mean called?

A) Standard error of the mean
B) Sampling error
C) Interval estimate
D) Point estimate

Question 15

A province-wide sample survey is to be made. First, the province is subdivided into counties. Seven counties are selected at random and further sampling is concentrated on these seven counties. What type of sampling is this?

A) Simple random
B) Non proportional
C) Cluster
D) Stratified

Question 16

Manufacturers were subdivided into groups by volume of sales. Those with more than $100 million in sales were classified as Class A large; those from $50 to $100 million as Class A medium size; and those between $25 and $50 million, and so on. Samples were then selected from each of these groups. What is this type of sampling called?

A) Simple random
B) Stratified random
C) Cluster
D) Systematic

Question 17

All possible samples of size n are selected from a population and the mean of each sample is determined. What is the mean of the sample means?

A) Exactly the same as the population mean
B) Larger than the population mean
C) Smaller than the population mean
D) Cannot be estimated in advance

Question 18

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spend studying per week. Based on a simple random sample, they surveyed 144 students. The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours. What is the standard error of the mean?

A) 0.83
B) 10
C) 0.5
D) 2

Question 19

i. A simple random sample assumes that each item or person in the population has an equal chance of being included. ii. We can expect some difference between sample statistics and the corresponding population parameters. This difference is called the sampling error.
iii. A sampling distribution of the means is a probability distribution consisting of a list of all possible sample means of a given sample size selected from a population and the probability of occurrence associated with each sample mean.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 20

An accounting firm is planning for the next tax preparation season. From last year's returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes. What is the standard error of the mean?

A) 14 minutes
B) 140 minutes
C) 1.4 minutes
D) 90 minutes

Question 21

Suppose a research firm conducted a survey to determine the average amount of money steady smokers spend on cigarettes during a week. A sample of 100 steady smokers revealed that the sample mean is $20 and the sample standard deviation is $5. What is the probability that a sample of 100 steady smokers spend between $19 and $21?

A) 0.4772
B) 0.0228
C) 0.9544
D) $20

Question 22

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15. i. What is the probability that a person would score 130 or more on the test?
ii. You enrolled in a class of 25 students. What is the probability that the class' average IQ exceeds 130?

A) 0.0228, 0.4987
B) 0.4772, 0.300
C) 0.4772, 0.0026
D) 0.0228, approximately zero

Question 23

An accounting firm is planning for the next tax preparation season. From last year's returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes. What is the probability that the mean completion time is between 1 and 2 hours, i.e., 60 and 120 minutes?

A) Approximately 1
B) 0.1664
C) 0.8336
D) 0.9676

Question 24

Prince Edward Island Fisheries and Environment has been feeding a special food to rainbow trout fingerlings in a pond. A sample of the weights of 40 trout revealed that the mean weight is 402.7 grams and the standard deviation 8.8 grams. What is the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams?

A) 0.3783
B) 0.0228
C) 1.0
D) 0.5

Question 25

An accounting firm is planning for the next tax preparation season. From last year's returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes. What assumptions do you need to make about the shape of the population distribution of all possible tax preparation times to make inferences about the average time to complete a tax form?

A) The population distribution is skewed to the right.
B) The population distribution is skewed to the left.
C) The population distribution is normal.
D) The shape of the population distribution does not matter.

Question 26

Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The average tread wear was found to be 50,000 miles with a standard deviation of 3,500 miles. What is the best estimate of the average tread life in miles for the entire population of these tires?

A) 50,000
B) 3,500
C) (50,000/100)
D) (3,500/100)

Question 27

An accounting firm is planning for the next tax preparation season. From last year's returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes. What is the probability that a sample mean would exceed 90 minutes per filing?

A) 1.0
B) 0.5
C) 1.96
D) Cannot be calculated based on the given information.

Question 28

Suppose a research firm conducted a survey to determine the average amount of money steady smokers spend on cigarettes during a week. A sample of 100 steady smokers revealed that the sample mean is $80 and the sample standard deviation is $20. What is the probability that a sample of 100 steady smokers spend between $76 and $84?

A) 0.4772
B) 0.0228
C) 0.9544
D) 0.3400
E) 0.9999

Question 29

The mean weight of trucks traveling on a particular section of I-475 is not known. A provincial highway inspector needs an estimate of the mean. He selects a random sample of 49 trucks passing the weighing station and finds the mean is 15.8 tonnes, with a standard deviation of the sample of 4.2 tonnes. What is probability that a truck will weigh less than 14.3 tonnes?

A) 0.0062
B) 0.3632
C) 0.1368
D) 0.4938

Question 30

The daily sales of a small retail store in Toronto for the last 365 days are normally distributed with a mean of $2,050, and a standard deviation of $300. i. What is the probability of daily sales exceeding $2,500?
ii. From a sample of 49 days, what is the probability of having a sample mean less than $2,500?

A) 0.4332, 0.0668
B) 0.0668, 0.9332
C) 0.4332, approximately 100%
D) 0.0668, Approximately 0%
E) 0.0668, Approximately 100%

Question 31

The daily sales of a small retail store in Toronto for the last 365 days are normally distributed with a mean of $2,050, and a standard deviation of $300. From a sample of 49 days, what is the probability of having a sample mean more than $2,000?

A) 0.3790
B) 0.8790
C) 0.121
D) Approximately zero
E) Approximately 100%

Question 32

For a population that is not normally distributed, the distribution of the sample means will:

A) be negatively skewed.
B) approach the normal distribution.
C) be positively skewed.
D) take the same shape as the population.

Question 33

i. If a population is not normally distributed, the sampling distribution of the sample means tends to approximate a normal distribution. ii. The Central Limit Theorem states that if the sample size n is sufficiently large, the sampling distribution of the means will be approximately normal no matter whether the population is normally distributed, skewed, or uniform.
iii. Based on the sampling distribution of the means and the central limit theorem, the sample mean can be used as a good estimator of the population mean, assuming that the size of the sample is sufficiently large.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement, but not (ii) or (iii).
C) (ii) is a correct statement, but not (i) or (iii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 34

As the size of the sample increases, what happens to the shape of the sampling means?

A) Cannot be predicted in advance
B) Approaches a normal distribution
C) Positively skewed
D) Negatively skewed

Question 35

An accounting firm is planning for the next tax preparation season. From last year's returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes. What is the probability that the mean completion time will be more than 120 minutes?

A) Approximately zero
B) 0.0832
C) 0.4168
D) 0.0162

Question 36

An experiment involves selecting a random sample of 256 middle managers at random for study. One item of interest is their mean annual income. The sample mean is computed to be $35,420 and the sample standard deviation is $2,050. What is the standard error of the mean?

A) $128.125
B) $138.36
C) $2,050
D) $8.01

Question 37

An accounting firm is planning for the next tax preparation season. From last year's returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes. What is the probability that average preparation time is between 80 and 90 minutes?

A) 0.7143
B) 0.7625
C) 0.2375
D) 0.2625

Question 38

What sample statistic is used to estimate a population parameter?

A) Parameter
B) Sampling error
C)
D) Interval estimate

Question 39

An accounting firm is planning for the next tax preparation season. From last year's returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes. What is the probability of finding a sample mean less than 80 minutes?

A) 0.7143
B) 0.7625
C) 0.2375
D) 0.0180

Question 40

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15. i. What is the probability that a person would score between 85 and 115?
ii. Given a class with 25 students, what is the probability that the class' average IQ score is between 85 and 115?

A) 0.3414, 0.0228
B) 0.6826, 0.9772
C) 0.6826, Approximately zero
D) 1.0, 0.9544

Question 41

Dawson's Repair Service orders parts from an electronic company who advertises its parts o be no more than 2% defective. What is the probability that Bill Dawson finds 4 or more parts out of a sample of 60 to be defective?

A) 4.85%
B) 0.49%
C) 15.62%
D) Almost 50%
E) 22.96%

Question 42

GreenFacts, a non-profit organization, reports that the average adult in Europe consumed 17 litres of alcohol last year. The standard deviation is 2.1 litres. If we randomly select 42 European adults, what is the probability that the sample mean is more than 17.8 litres?

A) 0.0068
B) 0.4873
C) 0.0058
D) 0.4863
E) 0.0680

Question 43

70% of North American women have pierced ears. For a survey of 49 women, what is the standard error?

A) 0.5
B) 0.7
C) 0.0655
D) 0.4245
E) 0.3

Question 44

Dawson's Repair Service orders parts from an electronic company who advertises its parts o be no more than 2% defective. What is the probability that Bill Dawson finds 3 or more parts out of a sample of 60 to be defective?

A) 4.85%
B) 0.485%
C) 15.62%
D) Almost 50%
E) 22.96%

Question 45

Dawson's Repair Service orders parts from an electronic company who advertises its parts o be no more than 2% defective. What is the probability that Bill Dawson finds 2 or more parts out of a sample of 60 to be defective?

A) 4.85%
B) 0.49%
C) 15.62%
D) Almost 50%
E) 22.96%

Question 46

A convenience store estimates that 25% of its customers come in to buy milk. What is the probability that out of the next 200 customers, 60 or fewer will buy milk?

A) 0.4484
B) 0.9484
C) 0.0516
D) Almost no chance
E) 0.0505

Question 47

Dawson's Repair Service orders parts from an electronic company who advertises its parts o be no more than 2% defective. What is the probability that Bill Dawson finds 4 or more parts out of a sample of 50 to be defective?

A) Almost 100%
B) Less than one half of one percent
C) About 1%
D) Almost 50%

Question 48

70% of North American women have pierced ears. In a survey of 49 women, what is the probability that less than 30 had pierced ears?

A) 0.0901
B) 0.5901
C) 0.9099
D) 0.4099

Question 49

Dawson's Repair Service orders parts from an electronic company who advertises its parts o be no more than 2% defective. What is the probability that Bill Dawson finds 3 or more parts out of a sample of 50 to be defective?

A) Almost 100%
B) 0.0217
C) 15.62%
D) Almost 50%
E) 34.38%

Question 50

The mean rent for a two-bedroom apartment in the Greater Toronto Area is $2,000 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 36 two-bedroom apartments and finding the mean to be under $1,800 per month? The standard deviation of the sample is $300.

A) 34.13%
B) 0%
C) 50%
D) 100%

Question 51

A study of a company's practice regarding the payment of invoices revealed that on the average an invoice was paid 20 days after it was received. The standard deviation equalled five days. A sample of 25 invoices is selected. Assuming that the distribution is normal, what percent of the sampled invoices were paid within 15 days of receipt?

A) 100%
B) 37.91%
C) 34.13%
D) 86.74%

Question 52

A new extended-life light bulb has an average service life of 750 hours, with a standard deviation of 50 hours. The shape of this distribution is unknown. From a sample of 100 light bulbs, about what percent of the bulbs will last more than 700 hours?

A) 100%
B) 34.13%
C) 84.13%
D) 50%

Question 53

The mean rent for a two-bedroom apartment in the Greater Toronto Area is $2,000 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 36 two-bedroom apartments and finding the mean to be under $1,500 per month? The standard deviation of the sample is $300.

A) 34.13%
B) 84.13%
C) 50%
D) 100%

Question 54

Dawson's Repair Service orders parts from an electronic company who advertises its parts o be no more than 2% defective. What is the probability that Bill Dawson finds 2 or more parts out of a sample of 50 to be defective?

A) Almost 100%
B) 0.0217
C) 0.1562
D) Almost 50%
E) 0.4783

Question 55

A retailer claims that 90% of its customers are "pleased" or "very pleased" with the customer service. In a survey of 300 customers taken last week, what is the probability that between 80% and 90% will be "pleased" or "very pleased" with the service?

A) 0.1736
B) 0.5736
C) 0.3464
D) Almost 100%
E) Almost 50%

Question 56

A retailer claims that 90% of its customers are "pleased" or "very pleased" with the customer service. In a survey of 300 customers taken last week, what is the probability that 84% or more will be "pleased" or "very pleased" with the service?

A) 0.1736
B) 0.5736
C) 0.3464
D) Almost 100%
E) Almost no chance

Question 57

It has been estimated that 25% of all university students switch majors within their first two years of starting classes. If a random sample of 500 third-year students is taken at a city university, what is an estimate of the probability that 20% or more had switched majors within their first two years?

A) 4951
B) 0049
C) 9951
D) 0.5059

Question 58

The mean rent for a two-bedroom apartment in the Greater Toronto Area is $2,000 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 36 two-bedroom apartments and finding the mean to be at least $1,500 per month? The standard deviation of the sample is $300.

A) 34.13%
B) 84.13%
C) 50%
D) 100%

Question 59

Alpha Corporation receives a shipment of flour every morning from their supplier. The flour is in 40 kg bags and Alpha will reject any shipment that is more than 4% underweight. The foreman samples 60 bags with each shipment and if the bags average more than 4% underweight, the whole shipment is returned to the supplier. Determine the value for the standard error of the proportion.

A) 0.0250
B) 0.0253
C) 0.00064
D) 0.0064
E) 0.08

Question 60

Alpha Corporation receives a shipment of flour every morning from their supplier. The flour is in 40 kg bags and Alpha will reject any shipment that is more than 5% underweight. The foreman samples 50 bags with each shipment and if the bags average more than 5% underweight, the whole shipment is returned to the supplier. Determine the value for the standard error of the proportion.

A) 0.03082
B) 0.0095
C) 0.00707
D) 0.00095
E) 0.09747

Question 61

(i. For populations scattered in a wide area, the preferred technique for sampling is simple random sampling. (ii) If the population can be divided into homogeneous subgroups, stratified random sampling is the best sampling method to use.
(iii) If every k-th item in the population sequence is selected, you are using systematic random sampling.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 62

(i. As the sample size (n) increases, the spread in the distribution of the sample means increases. (ii) If the sampling size equals the population size, the sampling error is zero.
(iii) If a population is normally distributed, the sampling distribution of the mean is normally distributed.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 63

(i. As the sample size (n) increases, the spread in the distribution of the sample means decreases. (ii) If the sampling size equals the population size, the sampling error is zero.
(iii) If a population is normally distributed, the sampling distribution of the mean is normally distributed.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 64

Alpha Corporation receives a shipment of flour every morning from their supplier. The flour is in 40 kg bags and Alpha will reject any shipment that is more than 5% underweight. The foreman samples 35 bags with each shipment and if the bags average more than 5% underweight, the whole shipment is returned to the supplier. Determine the value for the standard error of the proportion.

A) 0.0368
B) 0.00095
C) 0.0014
D) 0.0471
E) 0.00386

Question 65

(i. The type of sampling when a population is first divided into subgroups and then a sample is selected from each subgroup is called random sampling. (ii) Auditors may select every 20th file starting with say, the 5th file in the top drawer. Then file numbers 25, 45, 65, 85, are audited. This type of sampling is called systematic sampling.
(iii) The mean of a population is called a parameter.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 66

Alpha Corporation receives a shipment of flour every morning from their supplier. The flour is in 40 kg bags and Alpha will reject any shipment that is more than 5% underweight. The foreman samples 60 bags with each shipment and if the bags average more than 5% underweight, the whole shipment is returned to the supplier. Determine the value for the standard error of the proportion.

A) 0.02814
B) 0.01504
C) 0.00792
D) 0.08898
E) 0.1234

Question 67

(i. As the sample size (n) increases, the spread in the distribution of the sample means decreases. (ii) If the sampling size equals the population size, the sampling error is 1.
(iii) If a population is normally distributed, the sampling distribution of the mean is normally distributed.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 68

(i. The type of sampling when a population is first divided into subgroups and then a sample is selected from each subgroup is called stratified random sampling. (ii) Auditors may select every 20th file starting with say, the 5th file in the top drawer. Then file numbers 25, 45, 65, 85, are audited. This type of sampling is called systematic sampling.
(iii) The mean of a population is called a parameter.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 69

(i. The standard error of the mean is the standard deviation of the sampling distribution of the sample means.
(ii) The standard deviation of the sampling distribution of the mean is always larger than the standard deviation of the population under study.
(iii) For a sampling distribution of the means, 95% of the means would be between $\pm$ 1.96 standard deviations.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 70

Alpha Corporation receives a shipment of flour every morning from their supplier. The flour is in 40 kg bags and Alpha will reject any shipment that is more than 4% underweight. The foreman samples 60 bags with each shipment and if the bags average more than 4% underweight, the whole shipment is returned to the supplier. Determine the value for the standard error of the proportion.

A) 0.00132
B) 0.0253
C) 0.00064
D) 0.08898
E) 0.0250

Question 71

Alpha Corporation receives a shipment of flour every morning from their supplier. The flour is in 40 kg bags and Alpha will reject any shipment that is more than 4% underweight. The foreman samples 40 bags with each shipment and if the bags average more than 4% underweight, the whole shipment is returned to the supplier. Determine the value for the standard error of the proportion.

A) 0.03098
B) 0.00096
C) 0.00064
D) 0.02771
E) 0.0250

Question 72

Alpha Corporation receives a shipment of flour every morning from their supplier. The flour is in 40 kg bags and Alpha will reject any shipment that is more than 5% underweight. The foreman samples 36 bags with each shipment and if the bags average more than 5% underweight, the whole shipment is returned to the supplier. Determine the value for the standard error of the proportion.

A) 0.00132
B) 0.0363
C) 0.00792
D) 0.08898
E) 0.1234

Question 73

(i. The type of sampling when a population is first divided into subgroups and then a sample is selected from each subgroup is called stratified random sampling. (ii) Auditors may select every 20th file starting with say, the 5th file in the top drawer. Then file numbers 25, 45, 65, 85, are audited. This type of sampling is called cluster sampling.
(iii) The mean of a population is called a parameter.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 74

(i. For populations scattered in a wide area, the preferred technique for sampling is cluster sampling. (ii) If the population can be divided into homogeneous subgroups, stratified random sampling is the best sampling method to use.
(iii) If every k-th item in the population sequence is selected, you are using systematic random sampling.

A) (i), (ii), and (iii) are all correct statements
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 75

Alpha Corporation receives a shipment of flour every morning from their supplier. The flour is in 40 kg bags and Alpha will reject any shipment that is more than 4% underweight. The foreman samples 50 bags with each shipment and if the bags average more than 4% underweight, the whole shipment is returned to the supplier. Determine the value for the standard error of the proportion.

A) 0.00132
B) 0.000768
C) 0.00064
D) 0.02771
E) 0.0250

Question 76

(i. The standard error of the mean is the standard deviation of the sampling distribution of the sample means.
(ii) The standard deviation of the sampling distribution of the mean is always smaller than the standard deviation of the population under study.
(iii) For a sampling distribution of the means, 95% of the means would be between $\pm$ 1.96 standard deviations.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 77

(i. The standard error of the mean is the standard deviation of the sampling distribution of the sample means.
(ii) The standard deviation of the sampling distribution of the mean is always smaller than the standard deviation of the population under study.
(iii) For a sampling distribution of the means, 90% of the means would be between $\pm$ 1.96 standard deviations.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 78

(i. For populations scattered in a wide area, the preferred technique for sampling is cluster sampling. (ii) If the population can be divided into homogeneous subgroups, stratified random sampling is the best sampling method to use.
(iii) If every k-th item in the population sequence is selected, you are using cluster sampling.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.