Deck 15: Sample Size and Statistical Theory

Question 1

The population variance is a measure of the population dispersion, based on the degree to which a response differs from the population mean response.

Answer 1

True

Question 2

Two samples are drawn from the same population with a known variance, 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.

Answer 2

True

Question 3

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

Answer 3

False

Question 4

Bo Derek calculates that she needs a sample size of 200, given the estimated mean, accuracy variance and 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 5

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

Question 6

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

Question 7

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 8

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

Question 9

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

Question 10

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

Question 11

It does not make sense to use disproportionate sampling if one of the subgroups of the population is a relatively small percentage of the population

Question 12

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

Question 13

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 14

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 15

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 16

The two population characteristics of most interest to researchers are and The two population characteristics of most interest to researchers.

Question 17

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

Question 18

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

Question 19

Which of the following factors does the interval estimate depends on? sample size? a) sample size b) confidence level c) population standard deviation d) all of the above

Question 20

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

Question 21

Assume that is distributed normally with 11efcb9a_a811_8fc8_b057_bbe19516e4bb_TB7490_00 = 0, 11efcb9a_a811_8fc8_b057_bbe19516e4bb_TB7490_00² = 1.What is Pz = 1)?

A)0.8413
B)0.1587
C)0.3413
D)0.0025
E)None of the above
Use the following information for questions 26 through 28
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 11efcb9a_a811_8fc8_b057_bbe19516e4bb_TB7490_00_x = 8.0 and 11efcb9a_a811_8fc8_b057_bbe19516e4bb_TB7490_00_x = .5, n sample size) = 16.

Question 22

a point such that the probability of getting any other

Question 23

a 90 percent confidence interval cannot be determined

Question 24

a 90 percent confidence interval will be 9.36 and 10.64,

Question 25

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 26

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 27

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.
Use the following information for questions 15 through 17
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 == 500 pounds variance =11efcb99_9ab1_2495_b057_c73ffb27937d_TB7490_00² = 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.

Question 28

a point such that the probability of getting any other

Question 29

The probability that X₁ will exceed 9 ounces is closest to

A)0.3085
B)0.1587
C)0.1056
D)0.0256
E)0.0100

Question 30

a point such that the probability of getting any other

Question 31

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 32

a 95 percent confidence interval indicates the range
a.1
b.2
c.3
d.4
e.1 and 2

Question 33

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

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

Question 34

Consider the following data: _ X = 10 = 4 n = 25 The lower and upper limits of

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

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

A)0.3085
B)0.1587
C)0.1056
D)0.0256
E)0.0100

Question 37

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 _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 38

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 39

The standard error of the sample mean is

A)0.5
B)0.5 divided by 16
C)0.25 divided by 16
D)0.5 divided by 4
E)0.25

Question 40

Let the variance of a normally distributed random sample be 16.A point that is 8 units away from the mean is

Question 41

Which of the following factors does sample size depend on?

A)size of population, number of groups and subgroups within the sample
B)accuracy required of the results
C)cost of the sample
D)variability of the population
E)all of the above