gyu assignment questions part 2

Question 1

As the sample size ______________, the variation of the sampling distribution of x⎯⎯ ___________.

a) None of the other choices is correct.
b) increases, decreases
c) increases, remains the same
d) decreases, remains the same
e) decreases, decreases

Answer 1

b) increases, decreases

Question 2

it has been reported that the average time to download the home page from a government website was 0.9 seconds. Suppose that the download times were normally distributed with a standard deviation of 0.3 seconds. If random samples of 23 download times are selected, describe the shape of the sampling distribution and how it was determined.

a) skewed; the original population is not a normal distribution
b) cannot be determined with the information that is given
c) normal; the original population is normal
d) normal; size of sample meets the Central Limit Theorem requirement

Answer 2

c) normal and the original population is normal

Question 3

An unbiased estimate of σ^2 is _____.

a) x⎯⎯
b) σ
c) s
d) s^2

Answer 3

d) s^2

Question 4

The population of all _________________ proportions is described by the sampling distribution of pˆ

a) sample
b) population
c) random
d) observed

Answer 4

a) sample

Question 5

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. What is μx?

a) 5
b) 8.33
c) 0.833
d) 50

Answer 5

d) 50

Question 6

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as _______________.

a) sampling error
b) sampling distribution of the mean
c) the Central Limit Theorem
d) cluster sampling

Answer 6

c) the Central Limit Theorem

Question 7

The Central Limit Theorem states that as the sample size increases, the distribution of the sample ____________ approaches the normal distribution.

a) standard deviations
b) medians
c) variances
d) means

Answer 7

d) means

Question 8

Consider two population distributions labeled A and B. Distribution A is highly skewed and nonnormal, while distribution B is slightly skewed and near normal. In order for the sampling distributions of A and B to achieve the same degree of normality,

a) populations A and B will require the same sample size.
b) None of the other choices is correct.
c) population B will require a larger sample size.
d) population A will require a larger sample size.

Answer 8

d) population A will require a larger sample size.

Question 9

Consider a sampling distribution formed based on n = 3. The standard deviation of the population of all sample means σ x- is ______________ less than the standard deviation of the population of individual measurements σ.

a) sometimes
b) never
c) always

Answer 9

c) always

Question 10

Suppose that we will randomly select a sample of 146 measurements from a population having a mean equal to 24 and a standard deviation equal to 6.

Describe the shape of the sampling distribution of the sample mean x-.

Do we need to make any assumptions about the shape of the population?

Why or why not?

Answer 10

the shape of the sampling distribution of the sample mean x- will be normally distributed

we don’t need to make any assumptions about the shape of the distribution because the sample size is large

Question 11

The ______________ of a sample statistic is the probability distribution of the population of all possible values of the sample statistic.

a) probability
b) sampling Distribution of Sample Mean
c) observations
d) sample mean

Answer 11

b) sampling Distribution of Sample Mean

Question 12

he notation for the standard deviation of the sampling distribution of the sample mean is __________.

a) σx- or Sx-
b) σx
c) (σx-)/n
d) μ

Answer 12

a) σx- or Sx-

Question 13

When the level of confidence and sample size remain the same, a confidence interval for a population proportion, p, will be ______________ when pˆ(1−pˆ) is larger than when pˆ(1−pˆ) is smaller.

a) wider
b) neither wider nor narrower (they will be the same)
c) narrower

Answer 13

a) wider

Question 14

When establishing the confidence interval for the average weight of a cereal box, assume that the population standard deviation is known to be 2 ounces.

Based on a sample, the average weight of a sample of 20 boxes is 16 ounces.

The appropriate test statistic to use is ________.

a) χ
b) z
c) p
d) t

Answer 14

b) z

Question 15

As the significance level α increases, the width of the confidence interval _______________.

a) increases
b) stays the same
c) decreases

Answer 15

c) decreases

Question 16

When the sample size and the sample proportion p⎯⎯
remain the same, a 90 percent confidence interval for a population proportion p will be ______________ the 99 percent confidence interval for p.

a) wider than
b) equal to
c) narrower than

Answer 16

c) narrower than

Question 17

When constructing a confidence interval, as the confidence level required in estimating the mean increases, the width of the confidence interval ______________.

a) increases
b) stays the same
c) decreases

Answer 17

a) increases

Question 18

When constructing a confidence interval for a population mean,

if a population is normally distributed and a small sample is taken, then the distribution of X⎯⎯⎯
is based on the ____________ distribution.

a) z
b) neither the z nor the t distribution
c) t
d) both the z and the t distribution

Answer 18

c) t

Question 19

As the sample size n increases, the width of the confidence interval _______________.

a) stays the same
b) increases
c) decreases

Answer 19

c) decreases

Question 20

As standard deviation increases, sample size _____________ to achieve a specified level of confidence.

a) remains the same
b) decreases
c) increases

Answer 20

c) increases

Question 21

As the stated confidence level decreases, the width of the confidence interval _______________.

A) decreases

B) stays the same

C) increases

Answer 21

A) decreases

Question 22

Assuming the same level of significance α,

as the sample size increases, the value of tα/2 ___________ approaches the value of zα/2.

a) always
b) never
c) sometimes

Answer 22

a) always

Question 23

When solving for the sample size needed to compute a 95 percent confidence interval for a population proportion p, having a given error bound E, we choose a value of p⎯⎯ that

a) makes pˆ(1−pˆ) as close to .25 as reasonably possible.
b) makes pˆ(1−pˆ) as large as reasonably possible and makes pˆ(1−pˆ) as close to .25 as reasonably possible.
c) makes pˆ(1−pˆ) as close to .5 as reasonably possible.
d) makes pˆ(1−pˆ) as large as reasonably possible.
e) makes pˆ(1−pˆ) as small as reasonably possible

Answer 23

b) makes pˆ(1−pˆ) as large as reasonably possible and makes pˆ(1−pˆ) as close to .25 as reasonably possible.

Question 24

When the level of confidence and sample standard deviation remain the same,

a confidence interval for a population mean based on a sample of n = 100 will be ______________ a confidence interval for a population mean based on a sample of n = 50.

a) wider than
b) equal to
c) narrower than

Answer 24

c) narrower than

Question 25

The width of a confidence interval will be

a) narrower for 90 percent confidence than for 95 percent confidence.
b) wider when the sample standard deviation (s) is small than when s is large.
c) narrower for 99 percent confidence than for 95 percent confidence.
d) wider for a sample size of 100 than for a sample size of 50

Answer 25

a) narrower for 90 percent confidence than for 95 percent confidence.

Question 26

A confidence interval increases in width as

a) All of the other choices are correct.
b) n decreases.
c) s increases.
d) the level of confidence increases

Answer 26

a) All of the other choices are correct.

Question 27

When the sample size and sample standard deviation remain the same, a 99 percent confidence interval for a population mean, μ, will be _________________ the 95 percent confidence interval for μ

a) wider than
b) equal to
c) narrower than

Answer 27

a) wider than

Question 28

If everything else is held constant, decreasing the margin of error causes the required sample size to ____________.

a) increase
b) decrease
c) stay the same

Answer 28

a) increase

Question 29

When the level of confidence and the sample size remain the same,

a confidence interval for a population mean μ will be ________________ when the sample standard deviation s is small than when s is large.

a) neither wider nor narrower (they will be the same)
b) narrower
c) wider

Answer 29

b) narrower

Question 30

As the margin of error decreases, the width of the confidence interval _______________.

a) increases
b) decreases
c) stays the same

Answer 30

b) decreases

Question 31

A confidence interval for the population mean is an interval constructed around the ____________.

a) t test statistic
b) population mean
c) sample mean
d) z test statistic

Answer 31

c) sample mean

Question 32

In determining the sample size to estimate a population proportion,

as p approaches .5, the calculated value of the sample size ______________.

a) increases
b) decreases
c) stays the same

Answer 32

a) increases

Question 33

As the standard deviation (σ) decreases, the width of the confidence interval _______________.

a) increases
b) decreases
c) stays the same

Answer 33

b) decreases

Question 34

The exact spread of the t distribution depends on the _________.

a) standard deviation of the sample
b) sample size n
c) z distribution
d) number of degrees of freedom

Answer 34

d) number of degrees of freedom

Question 35

When determining the sample size,

if the value found is not an integer initially, you should ____________ choose the next highest integer value.

a) always
b) never
c) sometimes

Answer 35

a) always

Question 36

The t distribution approaches the _______________ distribution as the sample size ___________.

a) binomial, decreases
b) z, decreases
c) z, increases
d) binomial, increases

Answer 36

c) z, increases

Question 37

When the level of confidence and sample proportion pˆ remain the same,

a confidence interval for a population proportion p based on a sample of n = 100 will be ______________ a confidence interval for p based on a sample of n = 400.

a) equal to
b) narrower than
c) wider than

Answer 37

c) wider than

Question 38

Using the critical value rule,

if a two-sided null hypothesis cannot be rejected for a single mean at a given significance level,

then the corresponding one-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will ______________ be rejected at the same significance level

a) never
b) always
c) sometimes

Answer 38

c) sometimes

Question 39

Assuming that the null hypothesis is true,

the ______________ is the probability of observing a value of the test statistic that is at least as extreme as the value actually computed from the sample data

a) α
b) β
c) Type I error
d) p-value

Answer 39

d) p-value

Question 40

Using the p-value rule for a population proportion or mean, if the level of significance is less than the p-value, the null hypothesis is rejected.

a) True
b) False

Answer 40

b) False

Question 41

Using either the critical value rule or the p-value rule,

if a one-sided null hypothesis for a single mean cannot be rejected at a given significance level,

then the corresponding two-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will ______________ be rejected at the same significance level

a) never
b) always
c) sometimes

Answer 41

a) never

Question 42

Assuming a fixed sample size, as α (Type I error) decreases, β (Type II error) ___________.

a) decreases
b) randomly fluctuates
c) stays the same
d) increases

Answer 42

d) increases

Question 43

The null hypothesis is a statement that will be accepted only if there is convincing sample evidence that it is true.

a) True
b) False

Answer 43

b) False

By definition, the alternative or research hypothesis will be accepted only if there is convincing evidence that it is t

Question 44

Using the p-value rule,

if a null hypothesis is not rejected at a significance level of .05, it will _____________ be rejected at a significance level of .01

a) sometimes
b) always
c) never

Answer 44

c) never

Question 45

The level of significance, α, indicates the probability of rejecting a false null hypothesis.

a) True
b) False

Answer 45

b) False

The level of significance is the probability of rejecting a true null hypothesis

Question 46

When testing a hypothesis about a single mean,

if the sample size is 51 and the population standard deviation is known, the correct test statistic to use is ___________.

a) z
b) p-value
c) r
d) t

Answer 46

a) z

Question 47

As the Type II error, β,of a statistical test increases, the power of the test _____________.

a) stays the same
b) increases
c) decreases
d) randomly fluctuates

Answer 47

c) decreases

Question 48

When applying either the critical value rule or the p-value rule about a single mean,

other relevant factors held constant,

increasing the level of significance, α, from .05 to .10 will reduce the probability of a Type I error.

a) True
b) False

Answer 48

b) False

Increasing α will increase the probability of a Type I error.

Question 49

A null hypothesis is not rejected at a given level of significance.

As the assumed value of the mean gets further away from the true population mean, the Type II error will _____________.

a) stay the same
b) decrease
c) randomly fluctuate
d) increase

Answer 49

b) decrease

Question 50

Using the critical value rule,

if a two-sided null hypothesis is rejected for a single mean at a given significance level,

the corresponding one-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will ______________ be rejected at the same significance level.

a) sometimes
b) never
c) always

Answer 50

c) always

Question 51

The χ2 statistic from a contingency table with 6 rows and 5 columns will have

a) 25 degrees of freedom.
b) 24 degrees of freedom.
c) 30 degrees of freedom.
d) 5 degrees of freedom.
e) 20 degrees of freedom.

Answer 51

e) 20 degrees of freedom.

Question 52

An experiment consists of 400 observations and four mutually exclusive groups.

If the probability of a randomly selected item being classified into any of the four groups is equal, then the expected number of items that will be classified into group 1 is _____.

a) 100
b) 150
c) 125
d) 25

Answer 52

a) 100

(.25)(400) = 100

Question 53

In performing a chi-square goodness-of-fit test with multinomial probabilities,

the ___________ the difference between observed and expected frequencies, the higher the probability of concluding that the probabilities specified in the null hypothesis are correct

a) smaller
b) larger

Answer 53

a) smaller

Question 54

Which, if any, of the following statements about the chi-square test of independence is false?

a) All of the other statements about the chi-square test of independence are true.
b) The chi-square statistic is based on (r − 1)(c − 1) degrees of freedom, where r and c denote, respectively, the number of rows and columns in the contingency table.
c) The test is valid if all of the estimated cell frequencies are at least five.
d) The alternative hypothesis states that the two classifications are statistically independent.
e) If ri is the row total for row I and cj is the column total for column j, then the estimated expected cell frequency corresponding to row I and column j equals (ri)(cj)/n.

Answer 54

d) The alternative hypothesis states that the two classifications are statistically independent.

Question 55

The χ2 statistic is used to test whether the assumption of normality is reasonable for a given population distribution. The sample consists of 5,000 observations and is divided into 6 categories (intervals). The degrees of freedom for the chi-square statistic are

a) 5.
b) 3.
c) 4.
d) 6.
e) 4,999

Answer 55

a) 5

Degrees of freedom = k − 1, where k = number of intervals. Thus, df = 6 − 1 = 5

Question 56

The chi-square goodness-of-fit test will be valid if the average of the expected cell frequencies is ______________.

a) at least 5
b) greater than 0
c) between 0 and 5
d) less than 5
e) at least 1

Answer 56

a) at least 5

Question 57

The number of degrees of freedom associated with a chi-square test for independence based upon a contingency table with 4 rows and 3 columns is _____.

a) 5
b) 12
c) 6
d) 7

Answer 57

c) 6

df = (4 − 1)(3 − 1) = 6

Question 58

The chi-square goodness-of-fit is _________ a one-tailed test with the rejection region in the right tail.

a) always
b) never
c) sometimes

Answer 58

a) always

Question 59

The chi-square goodness-of-fit test for multinomial probabilities with 5 categories has _____ degrees of freedom.

a) 6
b) 4
c) 5
d) 3

Answer 59

b) 4

Question 60

When we carry out a chi-square test of independence,

as the differences between the respective observed and expected frequencies decrease,

the probability of concluding that the row variable is independent of the column variable

a) will be unaffected.
b) may decrease or increase depending on the number of rows and columns.
c) increases.
d) decreases.

Answer 60

c) increases.

Question 61

why does it increase the chances of having independent column in row variable in a chi-square test of independence whenever he differences between the respective observed and expected frequencies decrease?

Answer 61

When a chi-square test for independence is large (observed frequencies differ substantially from the expected frequencies), then doubt will be cast on the null hypothesis of independence

Therefore, a small difference will result in a small chi-square and lowers the likelihood of rejecting the null hypothesis of independence.