Deck 15: Sample Size and Statistical Theory

Question 1

If two random samples of equal size are drawn from the same population, we should expect the mean of both samples to be identical.

Answer 1

False

Question 2

A researcher takes a modest sample and, if results are worthwhile, opts for a larger sample.This type of sampling is called sequential sampling.

Answer 2

True

Question 3

The arithmetic average is the measurement of the sample mean.

Answer 3

True

Question 4

A 95 percent confidence interval will be smaller than a 90 percent confidence interval.

Question 5

If all members of the population have identical opinions on an issue, a sample of one is unsatisfactory.

Question 6

The size of a sample can be determined only by using statistical techniques.

Question 7

Two samples are drawn from the same population with a known variance, $\sigma$ ².If the sample sizes are 100 and 400, then the standard error of the mean of the former sample will be half that of the latter.

Question 8

The equation for the sample variance is 1 n S² = $\Sigma$ X_i - X )² n - 1

Question 9

Bo Derek calculates that she needs a sample size of 200, given the estimated mean, accuracy variance nd required Z-score.However, she learns that the variance is actually one-half of what she originally believed.Her required sample size will now be

A)100
B)800
C)400
D)50
E)none of the above

Question 10

If the population variance is 10 and the sample size is 16, then the standard error of the mean is 2.5.

Question 11

The two population characteristics of most interest to researchers are $\mu$ and $\sigma$ .

Question 12

If the allowed error is increased, the required sample size would decrease.

Question 13

The sample variance, S², can be used to estimate the population variation.

Question 14

It is sensible to use disproportionate sampling if one of the subgroups of the population is a relatively small percentage of the population

Question 15

What determines the statistical operations that can be performed on a scale type?

A)intransitivity property
B)invariance property
C)comparative property
D)isomorphic property

Question 16

The sample mean is not known, but it can be estimated from the population characteristics.

Question 17

If we wanted to be 95 percent confident that we wouldn't make an error of more than 1 unit in our estimate of $\mu$ or $\sigma$ = 2), we would need a sample size of approximately 16.

Question 18

If the population variance is 4, the sample standard deviation must be 2.

Question 19

The distribution which we say always assume to be "normal " or bell shaped is the

A)sampling distribution
B)population distribution
C)sample distribution
D)variance distribution
E)standard distribution

Question 20

When a complex multi-stage design is involved, a common approach is to replicate the entire sampling plan and get various independent estimates of the sample mean.

Question 21

A market research firm has been engaged to do a study of dishwashing detergents preferred by homemakers in San Francisco 800,000 population) as compared to those preferred in New York 8,000,000 population).In order to obtain results of about equal reliability in each city, the number of homemakers polled in New York should be

A)ten times the number polled in San Francisco.
B)10 or 3.16 times the number polled in San Francisco.
C)about the same as in San Francisco.
D)half the number polled in San Francisco.

Question 22

ABC Incorporated wants to find out the proportion of customers who would purchase their new product.They have decided to take a modest sample, look at the results, and then decide if more information, in the form of a larger sample, is needed.ABC is using

A)simple random sampling.
B)biased random sampling.
C)stratified sampling.
D)sequential sampling.
E)none of the above.

Question 23

Which of the following statements is true?

A)The sample size required to ensure 95 percent confidence limits will be smaller than that for 90 percent confidence limits.
B)The sample size required to ensure a smaller confidence interval will also be smaller.
C)The only way to reduce the width of a confidence interval is to reduce the confidence requirements.
D)The required sample size is dependent on å only.
E)The required sample size for given error and confidence levels is independent of the population size.

Question 24

The probability that a confidence level will include a population parameter is called

A)precision level
B)critical value
C)standard deviation
D)confidence level

Question 25

Two samples are drawn from the same population: Which of the following statements is true? _ _ 1-The distribution of X₁ will be taller than that of X₂. 2-The standard deviations of the two means are equal. 3- $\mu$ ₁ $\neq$$\mu$ ₂ 4-The two population variances are equal.

A)1
B)2
C)3
D)4
E)1 and 4

Question 26

Consider the following four statements: 1.The distribution of the mean of a random sample approaches the normal distribution as the sample size increases, only if the parent population is normally distributed. 2-The distribution of the mean of a random sample taken from a normal population is normal, irrespective of the sample size. 3-The distribution of the mean of a random sample taken from practically any population approaches the normal distribution as the sample size increases. 4-The distribution of the mean of a random sample taken from practically any population is normal, irrespective of the sample size. Which of the above statements is/are true?

A)Only 1
B)2 and 3
C)2 and 4
D)Only 3
E)None of the above

Question 27

Use the following information for questions
A soap factory produces 500-pound boxes of soap for industries.
However, the weight of the boxes varies somewhat due to the process.
Assume that the weight of each box is distributed normally with
mean = $\mu$ = 500 pounds variance = $\sigma$ ² = 25 pounds²
Quality control takes a random sample of 25 boxes per day.Let the
weight of these boxes be denoted as X₁, X₂, ..., X₂₅.

-What happens to the standard deviation of the sample mean, if we change the sample size from 25 to 100?

A)It is decreased by a factor of 4.
B)It is increased by a factor of 4.
C)It is decreased by a factor of 2.
D)It is decreased by a factor of 16.
E)None of the above.

Question 28

Use the following information for questions
A soap factory produces 500-pound boxes of soap for industries.
However, the weight of the boxes varies somewhat due to the process.
Assume that the weight of each box is distributed normally with
mean = $\mu$ = 500 pounds variance = $\sigma$ ² = 25 pounds²
Quality control takes a random sample of 25 boxes per day.Let the
weight of these boxes be denoted as X₁, X₂, ..., X₂₅.

-The probability that the sample mean lies between 498 and 502 is closest to

A).3174
B).9772
C).9544
D).3108
E).6826

Question 29

Means can only be meaningfully calculated on

A)nominal-or higher-scaled data
B)ratio-scaled data
C)interval-or ratio-scaled data
D)ordinal-or higher-scaled data

Question 30

Which of the following is set in advance for the statistical determination of sample size?

A)sample size
B)standard deviation
C)sampling frame
D)precision level

Question 31

Consider the following data: _ X = 10 $\sigma$ ² = 4 n = 25 The lower and upper limits of 1-a 90 percent confidence interval will be 9.36 and 10.64, respectively. 2-a 95 percent confidence interval will be 9.216 and 10.784, respectively. 3-a 90 percent confidence interval cannot be determined for the given data. 4-a 95 percent confidence interval indicates the range within which $\mu$ must lie.

A)1
B)2
C)3
D)4
E)1 and 2

Question 32

As the sample size becomes larger, the mean of the sampling distribution becomes

A)greater than the population mean
B)smaller than the population mean
C)equal to the population mean
D)double that of the population mean

Question 33

Let the variance of a normally distributed random sample be 16.A point that is 8 units away from the mean is 1-a point such that the probability of getting any other point further from the mean is less than 0.025. 2-a point such that the probability of getting any other point further from the mean is less than or equal to .95. 3-a point such that the probability of getting any other point further from the mean is greater than 0.025. 4-two standard deviations away from the mean.

A)1
B)2
C)3
D)4
E)1 and 4

Question 34

The standard error of the mean is the same as the

A)standard deviation of the population
B)standard deviation of the normal distribution
C)standard deviation of the sampling distribution
D)none of the above

Question 35

It is estimated that the proportion of Californians in favor of Proposition 5 is between 0.4 and 0.6.The sponsors of the proposition would like to sample Californians and get a 95 percent confidence interval for the true proportion of people in favor of Proposition 5.They want to restrict the error level to 5 percentage points.The required sample size is then

A)400.
B)40.
C)100.
D)1,000.
E)none of the above.

Question 36

Use the following information for questions
A soap factory produces 500-pound boxes of soap for industries.
However, the weight of the boxes varies somewhat due to the process.
Assume that the weight of each box is distributed normally with
mean = $\mu$ = 500 pounds variance = $\sigma$ ² = 25 pounds²
Quality control takes a random sample of 25 boxes per day.Let the
weight of these boxes be denoted as X₁, X₂, ..., X₂₅.

-The probability that X₈ is between 495 and 505 pounds is closest to

A).0228
B).3174
C).9772
D).6826
E).3830

Question 37

A distribution which tails off to the right and contains a few very large values is described as

A)negatively skewed
B)platykurtic
C)positively skewed
D)symmetric

Question 38

Which of the following isare.a statistics)?

A)sample mean
B)population median
C)population standard deviation
D)all the above

Question 39

Consider the following data from a random sample: 10 10 $\Sigma$$\bar{x}$ X _I = 70 $\Sigma$ X_I - X )² = 18 i=1 _

A)X = 7, S² = 2
B) $\mu$ = 7, $\sigma$ ² = 2 _
C)X = 7, $\sigma$ ² = 2
D)The population mean is 7 and S² = 2
E)It is not possible to estimate the population mean and standard deviation from the given information.

Question 40

Consider the following: For the given data:

A) $\mu$ = .6, $\sigma$ ² = 0, A = 0, B = 1, C = .3.
B) $\mu$ = 0, $\sigma$ ² =.6, A = 0, B = -1, C = .3.
C) $\mu$ = 0, $\sigma$ ² = .6, A = 0,B = 1, C= .3.
D) $\mu$ = 0, $\sigma$ ² = .6, A = .4,B = -1, C = .3.
E) $\mu$ = .6, $\sigma$ ² = 0, A = .4,B = 1,C = .3.

Question 41

Assume that $\mu$ is distributed normally with $\mu$ = 0, $\sigma$ ² = 1.What is Pz = 1)?

A).8413
B).1587
C).3413
D).0025
E)None of the above

Question 42

A college dean wants to determine the average time it takes a student to get from one class to the next.Preliminary studies have shown that it is reasonable to let $\sigma$ _t = 1.5 minutes the standard deviation of class travel times).What is the sample size which should be examined if the dean wants to assert with a probability of 95 percent that his estimate, the mean time of the random sample, will not be "off" by more than .25 minutes in either direction)? Choose the closest answer.

A)72 or more, but not less
B)81 or more, but not less
C)139 or more, but not less
D)200 or more, but not less
E)None of the above

Question 43

Use the following information for questions
Consider a meat packing plant which produces packages of frozen
steak.Let X be the weight ounces) and assume that X is normally
distributed with $\mu$ _x = 8.0 and $\sigma$ _x = .5, n sample size.= 16.

-Before the sample is drawn, the probability that the sample mean will exceed 9 ounces is closest to

A).3085
B).1587
C).1056
D).0256
E).0100

Question 44

Use the following information for questions
Consider a meat packing plant which produces packages of frozen
steak.Let X be the weight ounces) and assume that X is normally
distributed with $\mu$ _x = 8.0 and $\sigma$ _x = .5, n sample size.= 16.

-The probability that X₁ will exceed 9 ounces is closest to

A).3085
B).1587
C).1056
D).0256
E).0100

Question 45

Use the following information for questions
Consider a meat packing plant which produces packages of frozen
steak.Let X be the weight ounces) and assume that X is normally
distributed with $\mu$ _x = 8.0 and $\sigma$ _x = .5, n sample size.= 16.

-The standard error of the sample mean is

A).5
B).5 divided by 16
C).25 divided by 16
D).5 divided by 4
E).25