Deck 9: Hypothesis Testing

Question 1

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

Answer 1

A

Question 2

One-tailed alternatives are phrased in terms of:

A)ｹ
B)< or >
C)=
D)

Answer 2

B

Question 3

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

Answer 3

A

Question 4

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 5

Smaller 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 6

The value set for is known as:

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

Question 7

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 8

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 9

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 10

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 11

The ANOVA test is based on which assumptions?

A)The samples are independent and randomly selected from the populations
B)The populations are normally distributed
C)All population variances are equal
D)All of these options
E)None of these options

Question 12

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 13

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 14

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 15

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 16

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 17

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

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

Question 18

Which of the following values is not typically used for ?

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

Question 19

One-way ANOVA is often used in situations where:

A)there are two populations
B)randomly selected populations
C)randomized experiments with a single population
D)none of these options

Question 20

One-way ANOVA is used when analyzing the:

A)difference between more than two population means
B)results of a two-tailed test
C)results from a large sample
D)difference between two population variances

Question 21

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

Question 22

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 23

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

Question 24

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 25

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

Question 26

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

Question 27

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 28

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 29

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

Question 30

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

A)=
B)=
C)=
D)?
E)All of these options

Question 31

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

Question 32

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

Question 33

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 34

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

Question 35

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

Question 36

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 37

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 38

The alternative hypothesis is also known as the:

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

Question 39

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 40

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

Question 41

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 42

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

Question 43

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 if the populations are normal with equal variances.

Question 44

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

Question 45

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

Question 46

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

Question 47

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: , ,should be used.

Question 48

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

Question 49

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

Question 50

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

Question 51

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 52

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

Question 53

The Lilliefors test is used to test for normality.

Question 54

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

Question 55

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

Question 56

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 57

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

Question 58

The significance level also determines the rejection region.

Question 59

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 60

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

Question 61

The F-test of the analysis of variance requires that the populations are normally distributed with equal variances.

Question 62

If the p-value is sufficiently small for an ANOVA test,we can that all the population means are equal.

Question 63

The analysis of variance (ANOVA)technique analyzes the variance of the data to determine whether differences exist between the population means.

Question 64

(A)Given the information above,what is and for this comparison? Also,does this represent a one-tailed or a two-tailed test? Explain your answer.
(B)What are the degrees of freedom for the t-statistic in this calculation? Explain how you would calculate the degrees of freedom in this case.
(C)What is the assumption in this case that allows you to use the pooled standard deviation for this test?
(D)Using a 5% level of significance,is there sufficient evidence for Q-Mart to conclude that customers who use the Q-Mart card charge,on average,more than those who use another charge card? Explain your answer.
(E)Using a 1% level of significance,is there sufficient evidence for Q-Mart to conclude that customers who use the Q-Mart card charge,on average,more than those who use another charge card? Explain your answer.

Question 65

(A)If you were to conduct a hypothesis test to determine if greater than 50% of customers who use this Internet-based site are women,would you conduct a one-tail or a two-tail hypothesis test? Explain your answer,and state the appropriate null and alternative hypotheses.
(B)How many customers out of the 1000 sampled must have been women in this case?
(C)Using a 5% significance level,can the owner of this site conclude that women make up more than 50% of her customers? Explain your answer.
(D)If you were to use a 1% significance level,would the conclusion from (C)change? Explain your answer.

Question 66

(A)Use the information above to perform the test of equal variance.Explain how the ratio of sample variances is calculated.What type of distribution is used to test for equal variances? Also,would you conclude that the variances are equal or not? Explain.
(B)Based on your conclusion in (A),which test statistic should be used in performing a test for the existence of a difference between population means?
(C)Using a 5% level of significance,is there sufficient evidence to conclude that IS majors earn,on average,a higher annual starting salaries than their peers who major in Mktg?
(D)Using a 1% level of significance,is there sufficient evidence to conclude that IS majors earn,on average,a higher annual starting salaries than their peers who major in Mktg? Explain your answer.

Question 67

(A)Is there a significant difference in satisfaction between those who received their products in time for the holidays,and those who did not receive their products in time for the holidays? Test at the 0.01 level of significance.
(B)Find the p-value associated with the test in Question 110 and interpret its meaning.
(C)Based on the results of (A)and (B),if you were the marketing director of a company selling products online,what would you do to improve the satisfaction of the customers?

Question 68

An investor wants to compare the risks associated with two different stocks.One way to measure the risk of a given stock is to measure the variation in the stock's daily price changes.The investor obtains a random sample of 20 daily price changes for stock 1 and 20 daily price changes for stock 2.These data are shown in the table below.Show how this investor can compare the risks associated with the two stocks by testing the null hypothesis that the variances of the stocks are equal.Use = 0.10 and interpret the results of the statistical test.

Question 69

(A)State the appropriate null and alternative hypotheses in this situation.
(B)Test this CEO's belief at the =.05 significance level and report the p-value.Do you find statistical support for his hypothesis that the proportion of women in similar sales positions across the country is less than 40%?
(C)Suppose the sample size above is 100,instead of 50,and the sample proportion is again 0.36.Would this change your results in (B)? Explain your answer.

Question 70

In an ANOVA test,the alternative hypothesis is that at least one population mean is different from the others.

Question 71

A recent study of educational levels of 1000 voters and their political party affiliations in a Midwestern state showed the results given in the table below.Use = .10 and test to determine if party affiliation is independent of the educational level of the voters.

Question 72

(A)If you were to conduct a hypothesis test to determine if greater than 50% of customers prefer Coca-Cola to other brands,would you conduct a one-tail or a two-tail hypothesis test? Explain your answer.
(B)How many customers out of the 200 sampled must have favored Coke in this case?
(C)Using a 5% significance level,can the marketing consultant conclude that the proportion of customers who prefer Coca-Cola exceeds 50%? Explain your answer.
(D)If you were to use a 1% significance level,would the conclusion from Question 82 change? Explain your answer.

Question 73

(A)Can the sample size be determined from the information above? Yes or no? If yes,what is the sample size in this case?
(B)The firm believes that the mean life is actually greater than 1500 hours,should you conduct a one-tailed or a two-tailed hypothesis test? Explain your answer,and state the appropriate null and alternative hypotheses.
(C)What is the sample mean of this data? If you use a 5% significance level,would you conclude that the mean life of the light bulbs is typically more than 1500 hours? Explain your answer.
(D)If you were to use a 1% significance level in this case,would you conclude that the mean life of the light bulbs is typically more than 1500 hours? Explain your answer.

Question 74

(A)Is this two-sample data or paired data.Explain your answer.
(B)Specify an appropriate hypothesis test.
(C)Using a 10% level of significance,do the given sample data support that the firm's training programs is effective in increasing the new employee's computer skills?
(D)Using a 1% level of significance,do the given sample data support that the firm's training programs is effective in increasing the new employee's working knowledge of computing ?

Question 75

(A)Assume that the national average weekly grocery bill for a five-person family is $131.Is the sample evidence statistically significant? If so,at what significance levels can you reject the null hypothesis?
(B)For which values of the sample mean (i.e.,average weekly grocery bill)would you decide to reject the null hypothesis at the significance level? For which values of the sample mean would you decide to reject the null hypothesis at the 10% level of significance?

Question 76

(A)Are these measurements normally distributed? Summarize your results.
(B)Are there any weaknesses or concerns about your conclusions in (A)? Explain

Question 77

(A)Is there evidence of a significant difference in the average appraised values for single-family homes in the two Michigan cities? Use 0.05 level of significance.
(B)Have any of the assumptions made in (A)been violated? Explain.
(C)Construct a 95% confidence interval estimate of the difference between the population means of Lansing and Grand Rapids.
(D)Explain how to use the confidence interval in (C)to answer (A).

Question 78

(A)Construct a 90% confidence interval for the difference between the proportions of unacceptable assemblies generated by the two teams.
(B)Based on the confidence interval constructed in (A),is there sufficient evidence to conclude,at the 10% significance level,that the two teams differ with respect to their proportions of unacceptable assemblies?
(C)Is there sufficient evidence to conclude,at the 10% significance level,that the two teams differ with respect to their proportions of unacceptable assemblies? Conduct the appropriate hypothesis test.
(D)Calculate the p-value and explain how to use it for testing the null hypothesis of equal proportion.

Question 79

A sport preference poll yielded the following data for men and women.Use the 5% significance level and test to determine if sport preference and gender are independent.

Question 80

(A)Specify a hypothesis test to test the foundation's claim
(B)Compared to the most recent survey,is this sample evidence statistically significant at the 10% level?
(C)Compared to the most recent survey,is this sample evidence statistically significant at the 5% level?
(D)Report and interpret the p-value for this test
(E)Interpret the overall test for the foundation.