Deck 9: Hypothesis Testing

Question 1

Tests in which samples are not independent are referred to as matched pairs or paired samples.

Answer 1

True

Question 2

When testing the equality of two population variances,the test statistic is the ratio of the population variances;namely $$\sigma _ { 1 } ^ { 2 } / \sigma _ { 2 } ^ { 2 }$$
.

Answer 2

False

Question 3

A low p-value provides evidence for accepting the null hypothesis and rejecting the alternative.

Answer 3

False

Question 4

The Lilliefors test is used to test for normality.

Question 5

The rejection region is the set of sample data that leads to the rejection of the alternative hypothesis.

Question 6

A chi-square goodness-of-fit test can be used to test for normality.

Question 7

The analyst gets to choose the significance level $a$
.It is typically chosen to be 0.50,but it is occasionally chosen to be 0.05.

Question 8

The chi-square test for normality makes a comparison between the observed histogram and a histogram based on normality.

Question 9

The test statistic employed to test $H _ { 0 } : \sigma _ { 1 } ^ { 2 } / \sigma _ { 2 } ^ { 2 } = 1 \text { is } F = s _ { 1 } ^ { 2 } / s _ { 2 } ^ { 2 }$
,which is F distributed with $n _ { 1 } - 1 \text { and } n _ { 2 } - 1$
degrees of freedom.

Question 10

In conducting hypothesis testing for difference between two means when samples are dependent (paired samples),the variable under consideration is $$D$$
;the sample mean difference between the pairs.

Question 11

Side-by-side box-plots are typically a good way to begin the analysis when comparing two populations.

Question 12

The probability of making a Type I error and the level of significance $\alpha$
are the same.

Question 13

Sample evidence is statistically significant at the $a$
level only if the p-value is larger than $a$
.

Question 14

A one-tailed alternative is one that is supported by evidence in either direction.

Question 15

The p-value of a test is the probability of observing a test statistic at least as extreme as the one computed given that the null hypothesis is true.

Question 16

An example of a paired sample is the number of defective computer chips of a particular type from two different manufacturers.

Question 17

The significance level $\alpha$
also determines the rejection region.

Question 18

A test with a 0.05 significance level has a larger rejection region than a test with a 0.01 significance level.

Question 19

If a null hypothesis about a population mean $\mu$
is rejected at the 0.025 level of significance,then it must also be rejected at the 0.01 level.

Question 20

A professor of statistics refutes the claim that the proportion of Republican voters in Michigan is at most 45%.To test the claim,the hypotheses: $H _ { 0 } : p = 0.45 , H _ { a } : p \neq 0.45$
,should be used.

Question 21

A Type II error is committed when we incorrectly accept an alternative hypothesis that is false.

Question 22

Type I errors are usually considered more "costly" although this can lead to conservative decision making.

Question 23

A Type I error probability is represented by $\alpha$
;it is the probability of incorrectly rejecting a null hypothesis that is true.

Question 24

The form of the alternative hypothesis can be:

A) one-tailed
B) two-tailed
C) neither one nor two-tailed
D) one or two-tailed

Question 25

An alternative or research hypothesis is usually the hypothesis a researcher wants to prove.

Question 26

Which of the following signs is possible in an alternative hypothesis?

A) >
B) <
C) ≠
D) All of these options

Question 27

The power of a test is the probability of rejecting the null hypothesis when the alternative hypothesis is true.

Question 28

A test with a 0.10 significance level has a larger rejection region than a test with a 0.05 significance level.

Question 29

The test statistic for a hypothesis test of a population proportion is the z-value.

Question 30

A null hypothesis is a statement about the value of a population parameter.It is usually the current thinking,or "status quo".

Question 31

A null hypothesis can only be rejected at the 10% significance level if and only if:

A) a 90% confidence interval includes the hypothesized value of the parameter
B) a 90% confidence interval does not include the hypothesized value of the parameter
C) the null hypothesis is biased
D) the null hypotheses includes sampling error

Question 32

The p-value of a test is the smallest level of significance $a$
at which the null hypothesis can be rejected.

Question 33

The null hypothesis usually represents the:

A) theory the researcher would like to prove.
B) preconceived ideas of the researcher
C) perceptions of the sample population
D) status quo

Question 34

The idea of the chi-square test for independence is to:

A) compare the quantile-quantile (Q-Q)plot with what would be expected under independence
B) compare the actual counts in a contingency table with what would be expected under independence
C) compare the cumulative distribution with what would be expected under independence
D) None of these options

Question 35

In testing the difference between two population means using two independent samples,we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference $X _ { 1 } - X _ { 2 }$
if the populations are normal with equal variances.

Question 36

Lilliefors test for normality compare two cumulative distribution functions (cdf's): the cdf from a normal distribution and the cdf corresponding to the given data (called the empirical cdf).

Question 37

A test for independence is applied to a contingency table with 4 rows and 4 columns.The degrees of freedom for this chi-square test must equal 9.

Question 38

Which of the following statements are true regarding the chi-square goodness-of-fit test for normality?

A) The test does depend on which and how many categories we use for the histogram.
B) The test is not very effective unless the sample size is large,say,at least 80 or 100.
C) The test tends to be too sensitive if the sample size is really large.
D) None of these options
E) All of these options

Question 39

A Q-Q plot can be used to test for normality.

Question 40

An alternative hypothesis can have the signs >,<,or ≠.

Question 41

One-tailed alternatives are phrased in terms of:

A) ?
B) < or >
C) =
D)
$\leq \text { or } \geq$

Question 42

The p-value of a sample is the probability of seeing a sample with

A) at most as much evidence in favor of the null hypothesis as the sample actually observed.
B) at most as much evidence in favor of the alternative hypothesis as the sample actually observed.
C) at least as much evidence in favor of the null hypothesis as the sample actually observed.
D) at least as much evidence in favor of the alternative hypothesis as the sample actually observed.

Question 43

The test statistic in a hypothesis test for a population proportion is

A) t-value calculated from the sample
B) z-value calculated from the sample
C) F-value calculated from the sample
D) the sample proportion

Question 44

Of type I and type II error,which is traditionally regarded as more serious?

A) Type I
B) Type II
C) Type I and Type II are equally serious
D) Neither Type I or Type II is serious and both can be avoided

Question 45

The hypothesis that an analyst is trying to prove is called the:

A) elective hypothesis
B) alternative hypothesis
C) optional hypothesis
D) null hypothesis

Question 46

A type I error occurs when the:

A) null hypothesis is incorrectly accepted when it is false
B) null hypothesis is incorrectly rejected when it is true
C) sample mean differs from the population mean
D) test is biased

Question 47

A null hypothesis can only be rejected at the 5% significance level if and only if:

A) a 95% confidence interval includes the hypothesized value of the parameter
B) a 95% confidence interval does not include the hypothesized value of the parameter
C) the null hypothesis is biased
D) the null hypotheses includes sampling error

Question 48

If a teacher is trying to prove that new method of teaching economics is more effective than traditional one,he/she will conduct a:

A) one-tailed test
B) two-tailed test
C) point estimate of the population parameter
D) confidence interval

Question 49

A two-tailed test is one where:

A) results in only one direction can lead to rejection of the null hypothesis
B) negative sample means lead to rejection of the null hypothesis
C) results in either of two directions can lead to rejection of the null hypothesis
D) no results lead to the rejection of the null hypothesis

Question 50

Which of the following values is not typically used for $a$
?

A) 0.01
B) 0.05
C) 0.10
D) 0.50

Question 51

The alternative hypothesis is also known as the:

A) elective hypothesis
B) optional hypothesis
C) research hypothesis
D) null hypothesis

Question 52

Which of the following values is typically used for $a$
?

A) 0.50
B) 0.40
C) 0.30
D) 0.10

Question 53

Larger p-values indicate more evidence in support of the:

A) null hypothesis
B) alternative hypothesis
C) quality of the researcher
D) None of these options

Question 54

A type II error occurs when:

A) the null hypothesis is incorrectly accepted when it is false
B) the null hypothesis is incorrectly rejected when it is true
C) the sample mean differs from the population mean
D) the test is biased

Question 55

The chi-square goodness-of-fit test can be used to test for:

A) significance of sample statistics
B) difference between population means
C) normality
D) difference between population variances

Question 56

The power of a test is the probability that we

A) reject the null hypothesis when the alternative hypothesis is false
B) reject the null hypothesis when the alternative hypothesis is true
C) accept the null hypothesis when the alternative hypothesis is false
D) accept the null hypothesis when the alternative hypothesis is true

Question 57

The null and alternative hypotheses divide all possibilities into:

A) two sets that overlap
B) two non-overlapping sets
C) two sets that may or may not overlap
D) as many sets as necessary to cover all possibilities

Question 58

Which of the following statements are true of the null and alternative hypotheses?

A) Exactly one hypothesis must be true
B) Both hypotheses must be true
C) It is possible for both hypotheses to be true
D) It is possible for neither hypothesis to be true

Question 59

The value set for $a$
Is known as:

A) the rejection level
B) the acceptance level
C) the significance level
D) the error in the hypothesis test

Question 60

An informal test for normality that utilizes a scatterplot and looks for clustering around a 45° line is known as a(n):

A) Lilliefors test
B) empirical cumulative distribution function
C) p-test
D) quantile-quantile plot

Question 61

In statistical analysis,the burden of proof lies traditionally with the:

A) alternative hypothesis
B) null hypothesis
C) analyst
D) facts presented to the statistical analyst

Question 62

Which pair of the following tests is used to test for normality?

A) A t-test and an ANOVA test
B) An Empirical cumulative distribution function test and an F-test
C) A Chi-Square test and a Lilliefors test
D) A Quantile-Quantile plot and a p-value test

Question 63

A p-value is considered "convincing" if it is:

A) less than 0.01
B) between 0.01 and 0.05
C) between 0.05 and 0.10
D) greater than 0.10