Deck 9: Hypothesis Testing

Question 1

The burden of proof is traditionally on the null hypothesis.

Answer 1

False

Question 2

The significance level also determines the rejection region.

Answer 2

True

Question 3

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

Answer 3

False

Question 4

If a null hypothesis is rejected at the 0.025 level of significance,then it must also be rejected at the 0.01 level.

Question 5

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

Question 6

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

Question 7

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 8

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

Question 9

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

Question 10

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

Question 11

The alternative hypothesis always contains a statement of inequality,such as "less than","greater than",or "not equal to".

Question 12

The alternative hypothesis,or research hypothesis,is the hypothesis that the analyst is attempting to prove.

Question 13

The null hypothesis always contains a statement of equality,like "equal to","less than or equal to",or "greater than or equal to".

Question 14

A professor of statistics doubts the claim that the proportion of Republican voters in Michigan is at most 45%.To test the claim,the hypotheses: , ,should be used.

Question 15

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

Question 16

If a null hypothesis is rejected at the 0.01 level of significance,then it will also be rejected at the 0.025 level.

Question 17

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

Question 18

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

Question 19

The analyst gets to choose the significance level .It is typically chosen to be 0.50,but it is occasionally chosen to be 0.01.

Question 20

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

Question 21

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

Question 22

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

Question 23

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

Question 24

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

A)alternative hypothesis.
B)null hypothesis.
C)analyst.
D)p-value.

Question 25

The test statistic employed to test is ,which is F distributed with degrees of freedom.

Question 26

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 is 9.

Question 27

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

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 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 of the situation being studied.

Question 30

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

Question 31

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

Question 32

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

Question 33

When testing the equality of two population variances,the test statistic is the ratio of the population variances; namely .

Question 34

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 35

The F distribution is a skewed distribution useful for testing equality of variances.

Question 36

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

Question 37

The Lilliefors test is used to test for normality.

Question 38

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

Question 39

The chi-square test for normality makes a comparison between the observed histogram and a histogram based on normality with the same mean and standard deviation of that of the sample data.

Question 40

The hypothesis that an analyst is trying to prove is called the _____ hypothesis.

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

Question 41

The form of the alternative hypothesis can be

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

Question 42

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 43

The p-value of a sample is the probability of seeing a sample with at _____ hypothesis as the sample actually observed.

A)most as much evidence in favor of the null
B)most as much evidence in favor of the alternative
C)least as much evidence in favor of the null
D)least as much evidence in favor of the alternative

Question 44

A 95% confidence interval can be used to reject the null hypothesis of a two-sided test 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 less than 0.05.
D)the null hypotheses falls in the rejection region.

Question 45

Which sign is possible in an alternative hypothesis?

A)>
B)<
C)≠
D)All of these signs are possible

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 procedure is fundamentally biased.

Question 47

A type II 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 procedure itself is fundamentally biased.

Question 48

The alternative hypothesis is also known as the _____ hypothesis.

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

Question 49

One-tailed alternative hypotheses use the _____ symbol.

A)≠
B)< or >
C)=
D)

Question 50

Smaller p-values indicate more evidence in support of

A)the null hypothesis.
B)the alternative hypothesis.
C)the quality of the researcher.
D)none of these choices.

Question 51

A teacher who is trying to determine if the evidence supports the fact that a new method of teaching economics is more effective than a traditional one will conduct a _____ test.

A)one-tailed
B)two-tailed
C)multi-tailed
D)paired

Question 52

Which of the following values is not typically used for ?

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

Question 53

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

A)Type I is considered to be more serious.
B)Type II is considered to be more serious.
C)Type I and Type II are equally serious.
D)The situation determines which error is more serious.Sometimes type I errors are more serious and sometimes type II errors are more serious.

Question 54

Larger p-values indicate more evidence in support of the

A)null hypothesis.
B)alternative hypothesis.
C)type II error.
D)type I error.

Question 55

The power of a test is the probability that we _____ the null hypothesis when the alternative hypothesis is _____.

A)reject.false
B)reject.true
C)accept,false
D)accept,true

Question 56

A two-tailed test is one where _____ lead to rejection of the null hypothesis.

A)results in only one direction can
B)negative sample means
C)results in either of two directions can
D)no results

Question 57

The value set for is known as the

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

Question 58

Which of the following values is a common significance level?

A)0.50
B)0.40
C)0.30
D)0.05

Question 59

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 60

A sample result is considered "convincing" if the p-value 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.

Question 61

Which of the following statements is 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 choices is true.
E)Choices a,b,and c are all true.

Question 62

What is the idea behind the chi-square test for independence?

A)To compare the quantile-quantile (Q-Q)plot with what would be expected under independence
B)To compare the actual counts in a contingency table with what would be expected under independence
C)To compare the cumulative distribution with what would be expected under independence
D)To compare the normal distribution with a chi-squared distribution

Question 63

A 90% confidence interval can be used to reject the null hypothesis of a two-sided test 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 less than 0.05.
D)the null hypotheses includes sampling error is greater than 0.05.

Question 64

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 65

A restaurant manager claims that food servers at this restaurant make at least $15 per hour in tips.A random sample of 50 hours shows the mean amount of tips to be $12 per hour with standard deviation $0.75 per hour.What is the value of the test statistic that can be used to determine if there is convincing evidence that the mean amount of tips made per hour is less than the manager claimed?

A)t = -7.165
B)t = -0.566
C)t = 9.172
D)t = -0.08

Question 66

A test for a population mean has _____ degrees of freedom.

A)n + 1
B)n - 1
C)n
D)n - 2

Question 67

Which pair of 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 68

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 69

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

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 70

What type of test is used to determine if the population mean is equal to a hypothesized value?

A)t test
B)z test
C)F test
D)Chi-squared test