Deck 5: Hypothesis Testing and Statistical Inference

Question 1

If the confidence coefficient is 0.9,________.

A)we expect that 9 samples out of 100 will support the null hypothesis
B)we expect that 90 out of 100 samples will support the null hypothesis
C)we expect that 10 samples out of 100 will support the null hypothesis
D)we expect that all 100 samples will support the null hypothesis

Answer 1

we expect that 90 out of 100 samples will support the null hypothesis

Question 2

A Type I error occurs when ________.

A)the null hypothesis is actually false,but the hypothesis test incorrectly fails to reject it
B)the null hypothesis is actually true,and the hypothesis test correctly fails to reject it
C)the null hypothesis is actually false,and the hypothesis test correctly reaches this conclusion
D)the null hypothesis is actually true,but the hypothesis test incorrectly rejects it

Answer 2

the null hypothesis is actually true,but the hypothesis test incorrectly rejects it

Question 3

Read the following scenario and select the correct answer. There is a large range of starting salaries among software engineers.Sample statistics have been collected to determine if patterns emerge that can help explain this variability.It was found that the mean starting income for men is $42,000 and the mean starting income for women is $52,000.What conclusions can you make from this information?

A)The difference between mean starting salary for men and women is not random.
B)Women are more qualified than men.
C)Men are not compensated fairly.
D)It would be inappropriate to draw conclusions without first formulating a hypothesis and testing that hypothesis.

Answer 3

It would be inappropriate to draw conclusions without first formulating a hypothesis and testing that hypothesis.

Question 4

Hypothesis testing is a technique that allows you to draw statistically valid conclusions about ________.

A)random errors
B)sample statistics
C)population parameters
D)individuals

Question 5

The null hypothesis is denoted by ________.

A)H_N
B)H₀
C)H₁
D)H_A

Question 6

The alternative hypothesis ________.

A)describes an existing theory or belief that is accepted as correct in the absence of contradictory data.
B)is based on new information provided by population data.
C)is based on new information provided by sample data.
D)is not deemed to be an important part of inferential statistics.

Question 7

In hypothesis testing,the null and the alternative hypotheses are ________.

A)not mutually exclusive
B)mutually exclusive
C)always false
D)always true

Question 8

Which of the following is not a step in hypothesis testing?

A)formulating the hypotheses to test
B)selecting a level of significance
C)collecting data,summarizing,and reporting in a table
D)determining a decision rule on which to base a conclusion

Question 9

The confidence coefficient is ________.

A)the probability of correctly failing to reject the null hypothesis
B)the probability of making a Type II error
C)the probability of making a Type I error
D)the probability of correctly rejecting the null hypothesis

Question 10

The confidence coefficient is denoted by ________.

A)1 - β / 2
B)1 - β
C)1 - P(A)
D)1 - α

Question 11

The power of the test has a value of ________.

A)1 - α
B)1 + β
C)1 - β
D)α - β

Question 12

Hypothesis testing involves drawing inferences about two contrasting ________ relating to the value of a population parameter.

A)theorems
B)data sets
C)assumptions
D)propositions

Question 13

Statistical inference is the process of drawing conclusions about ________ from sample data.

A)surveys
B)populations
C)individuals
D)sampling errors

Question 14

The alternative hypothesis is denoted by ________.

A)H_N
B)H₀
C)H₁
D)H_Al

Question 15

If we fail to reject the null hypothesis,________.

A)we have found evidence to support the alternative hypothesis
B)the null hypothesis is proved to be true
C)we have only failed to find evidence to support the alternative hypothesis
D)the hypothesis test is inconclusive

Question 16

The null hypothesis ________.

A)describes an existing theory or belief that is accepted as correct in the presence of contradictory data
B)describes an existing theory or belief that is accepted as correct in the absence of contradictory data
C)is based on new information provided by sample data
D)is based on new information provided by population data

Question 17

Hypothesis testing can result in ________ different outcomes.

A)three
B)two
C)five
D)four

Question 18

A helpful analogy of hypothesis testing might be the concept of ________.

A)the U.S.legal system-innocent until proven guilty
B)better safe than sorry.
C)the theory of relativity
D)the central limit theorem

Question 19

Hypothesis testing always assumes that ________.

A)the alternative hypothesis is true
B)the null hypothesis is true
C)the probability of the null hypothesis being true is less than 50%
D)the probability of the alternative hypothesis being true is less than 50%

Question 20

The probability of making a Type I error is generally denoted by ________.

A)α
B)β
C)ξ
D)µ

Question 21

Use the below information to answer the following question(s).
The following table provides data on a sample of customers who visited a local restaurant.The restaurant owner believes that the average profit per customer exceeds $25.
Which of the following is the test statistic?

A)1.717
B)-1.867
C)1.867
D)-1.826

Question 22

The hypothesized sampling distribution of the test statistic is divided into ________ parts.

A)four
B)two
C)six
D)three

Question 23

Use the below information to answer the following question(s).
The following table provides data on a sample of customers who visited a local restaurant.The restaurant owner believes that the average profit per customer exceeds $25.
Which of the following is the conclusion?

A)The null hypothesis that the average profit per customer exceeds $25 cannot be rejected.
B)The null hypothesis that the average profit per customer does not exceed $25 is rejected.
C)The null hypothesis that the average profit per customer does not exceed $25 cannot be rejected.
D)The null hypothesis that the average profit per customer exceeds $25 is rejected.

Question 24

What is the appropriate alternative hypothesis for the null hypothesis,H₀: mean production cost = $2.00?

A)H₁: mean production cost > $2.00
B)H₁: mean production costs < $2.00
C)H₁: mean production costs ≥ $2.00
D)H₁: mean production costs ≠ $2.00

Question 25

In general,whenever p-value is less than α,________.

A)we reject the null hypothesis
B)we choose a different level of significance
C)we fail to reject the null hypothesis
D)the hypothesis test is inconclusive

Question 26

The rejection region is defined by ________.

A)a critical value
B)the power of the test
C)the probability of a Type II error
D)the sample size

Question 27

A one-tailed test is employed when the null hypothesis ________.

A)is structured as "≠"
B)specifies a direction of relationship
C)is structured as "="
D)falls in the upper tail of the distribution

Question 28

The p-value of a one sample t-test is dependent on the ________.

A)degrees of freedom
B)critical value of t
C)level of significance
D)power of the test

Question 29

Which of the following is the commonly used significance level for α,in most business applications?

A)0.5
B)0.25
C)0.05
D)0.0005

Question 30

Use the below information to answer the following question(s).
The following table provides data on a sample of customers who visited a local restaurant.The restaurant owner believes that the average profit per customer exceeds $25.
Which of the following is the critical value using a level of significance of 0.05?

A)1.717
B)-1.717
C)1.7139
D)-2.0739

Question 31

The power of the test represents the ________.

A)probability of correctly failing to reject the null hypothesis when it is indeed true
B)probability of incorrectly rejecting the null hypothesis when it is actually true
C)probability of incorrectly failing to reject the null hypothesis when it is actually false
D)probability of correctly rejecting the null hypothesis when it is indeed false

Question 32

In one-sample tests for means,the t-Test Statistic is calculated using the formula ________.

A)t =
B)t =
C)_{t =}
D)t =

Question 33

Use the below information to answer the following question(s).
The following table provides data on a sample of customers who visited a local restaurant.The restaurant owner believes that the average profit per customer exceeds $25.
Formulate the null and the alternative hypotheses to determine if the data supports the restaurant owner's claim.

A)H₀: The average profit per customer = $25 H₁: The average profit per customer ≠ $25
B)H₀: The average profit per customer ≤ $25 H₁: The average profit per customer > $25
C)H₀: The average profit per customer ≥ $25 H₁: The average profit per customer < $25
D)H₀: The average profit per customer > $25 H₁: The average profit per customer ≤ $25

Question 34

The t-Test Statistic has a t distribution with ________ degrees of freedom.

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

Question 35

If the null hypothesis is false,it is more likely that the test statistic will ________.

A)fall into the nonrejection region
B)not follow the uniform distribution
C)fall into the rejection region
D)not follow the normal distribution

Question 36

The Excel function Z.TEST returns the ________.

A)one-tailed p-value of a Z-test
B)right‐tailed critical value of Z
C)two-tailed p-value of a Z-test
D)left‐tailed critical value of Z

Question 37

Another term for p-value is ________.

A)degrees of freedom
B)random effect
C)probability density function
D)observed significance level

Question 38

The decision to reject or fail to reject a null hypothesis is based on computing a ________ from sample data.

A)population parameter
B)critical value
C)level of significance
D)test statistic

Question 39

Two-tailed tests ________.

A)have only lower critical values
B)have only upper critical values
C)have both upper and lower critical values
D)do not have any critical values

Question 40

In most practical applications,the population standard deviation will not be known but it is estimated from the ________.

A)population
B)sample
C)test statistic
D)t-distribution

Question 41

The test statistic for a one-sample test for proportions is ________.

A)t =
B)Z =
C)Z =
D)t =

Question 42

Which of the following is the conclusion?

A)We reject H₀ that the proportion of female managers is the same as the proportion of male managers.
B)We should not reject H₀ that the proportion of female managers is not the same as the proportion of male managers.
C)We reject H₀ that the proportion of female managers is not the same as the proportion of male managers.
D)We should not reject H₀ that the proportion of female managers is the same as the proportion of male managers.

Question 43

The power curve shows the power of the test as a function of ________.

A)significance level
B)sample size
C)true mean
D)confidence level

Question 44

Compute the 99% confidence interval estimate of the difference between the two proportions.[Hint: Use PHStat]

A)(0.139,-0.326)
B)(0.084,-0.270)
C)(-0.084,0.270)
D)(-0.139,0.326)

Question 45

An online retailer wanted to see if purchasing patterns were different between male consumers and female consumers.Males were found to have spent a mean of $85 per month on online purchases,whereas females were found to have spent a mean of $78 per month.An independent samples t-test was conducted to assess the observed difference between the two groups of consumers.A two-tailed test was applied.The value of the t-Test Statistic for the observed differences was -4.7,where the p-value is less than 0.0002.What conclusion can be made about the observed difference?

A)There is a statistically significant difference between the two groups of consumers.
B)There is statistically no significant difference between the two groups of consumers.
C)The independent samples t-test is not the appropriate hypothesis-testing procedure.
D)There is not sufficient information to conclude.

Question 46

Increasing the sample size is one way to ________.

A)reduce β
B)reduce the power of the test
C)increase the standard error of the mean
D)determine the exact β value

Question 47

Use the below information to answer the following question(s).
A company wishes to test whether the proportion of female managers is the same as the proportion of male managers.The following table provides data for a sample of employees.
Which of the following is the test statistic? [Hint: Use PHStat]

A)1.96
B)-1.04
C)-1.96
D)1.04

Question 48

The one-sample test for the variance employs the ________.

A)chi-square test for variance
B)ANOVA (Analysis of Variance)
C)Z-test
D)t-test

Question 49

In two‐sample test for means with paired samples,the test statistic is given by ________.

A)Z =
B)t =
C)t =
D) =

Question 50

The probability of a Type I error can be specified by the investigator.The probability of a Type II error is ________.

A)one minus the probability of Type I error
B)the result of the hypothesis test itself
C)also specified by the investigator
D)not specified by the investigator but computed using the power of the test

Question 51

PHStat has a tool for conducting the two-sample hypothesis tests for proportions.The test is called ________.

A)Z-test for differences in two means
B)chi-square test for differences in two proportions
C)Z-test for the proportions
D)Z- test for differences in two proportions

Question 52

Use the below information to answer the following question(s).
A company wishes to test whether the proportion of female managers is the same as the proportion of male managers.The following table provides data for a sample of employees.
Formulate the null and the alternative hypotheses to determine if the proportion of female managers is the same as the proportion of male managers.

A)H₀: π_females - π_males ≠ 0 H₁: π_females - π_males = 0
B)H₀: π_females - π_males ≤ 0 H₁: π_females - π_males > 0
C)H₀: π_females - π_males = 0 H₁: π_females - π_males ≠ 0
D)H₀: π_females - π_males ≥ 0 H₁: π_females - π_males < 0

Question 53

In the test statistic for a one-sample test for proportion,π₀ is the ________.

A)sample proportion
B)population proportion
C)hypothesized proportion value
D)standard error of the sampling distribution of the proportion

Question 54

A one-sample test for proportions employs the ________.

A)t-test
B)chi-square test
C)Z-test
D)F-test

Question 55

When conducting two-sample tests for means with independent samples,________.

A)it is always assumed that the population variances are equal
B)the test for equality of variances is conducted,and if the variances are not equal the t-test in Excel should not be used
C)the test for equality of variances is conducted to determine if the variances are equal and thereby choose the appropriate t-test in Excel
D)it is always assumed that the population variances are unequal

Question 56

To determine if there was a statistically significant difference in the means of two independent groups,which statistical tool would one be most likely to employ to assess the significance of any observed difference?

A)paired samples t-test
B)chi-square test for independence
C)Levene's test for homogeneity of variances
D)independent samples t-test

Question 57

To assess the effect of an intervention such as the productivity of an employee before and after a training class,one would conduct a(n)________.

A)independent samples t-test
B)ANOVA
C)paired samples t-test
D)F-test

Question 58

The chi‐square test statistic for a one-sample test for the variance is ________.

A) = (n - 1) /
B) = (n - 1)s /
C) = (n - 1) /
D) = (n - 1) /

Question 59

Identify the p-value.

A)0.1483
B)0.2966
C)0.8517
D)0.7034

Question 60

The power of the test depends on ________.

A)the true value of the population mean
B)the level of confidence used
C)the sample size
D)all of the above

Question 61

ANOVA requires ________ assumptions.

A)no
B)two
C)three
D)four

Question 62

When the assumptions underlying ANOVA are violated,________ is used.

A)the Tukey-Kramer multiple comparison procedure
B)the Levene test
C)a nonparametric test
D)a chi-square test

Question 63

The probability of making a Type I error is called the level of significance of the test.

Question 64

The Excel function CHISQ.TEST()will return the ________.

A)probability associated with a t-Test Statistic and the appropriate degrees of freedom
B)probability associated with the degree of linearity observed within the groups
C)test for independence: the value from the chi-square distribution for the statistic and the appropriate degrees of freedom
D)left-tailed probability of the chi-square distribution

Question 65

What test statistic is evaluated when testing for equality of variances?

A)t
B)Z
C)χ²
D)F

Question 66

The confidence coefficient is the probability of incorrectly failing to reject the null hypothesis.

Question 67

The Tukey-Kramer multiple comparison procedure allows an investigator to ________.

A)evaluate t-tests,ANOVA,regression,and other tests to determine which statistical tool is best for the data at hand
B)determine which of the means are significantly different,once ANOVA identifies that there is a significant difference among the means of multiple populations
C)determine if the means of several different groups are equal when the assumptions underlying ANOVA are violated
D)determine if the means of several different groups are equal,similar to the ANOVA

Question 68

The area that overlaps the hypothesized distribution in the acceptance region is α,the probability of a Type I error.

Question 69

In statistical terminology,educational level is an example of a ________.

A)continuous variable
B)residual
C)factor
D)dependent variable

Question 70

ANOVA allows us to compare the ________ of several different groups.

A)variances
B)means
C)distributions
D)proportions

Question 71

Which of the following can be the null hypothesis for a research study that would employ the chi-square test for independence?

A)H₀: gender and SUV ownership are dependent
B)H₀: gender and SUV ownership are independent
C)H₀: μ_gender = μ_{SUV ownership}
D)H₀: σ²_gender = σ²_{SUV ownership}

Question 72

The closer the observed frequencies are to the expected frequencies in each cell of the contingency table ________.

A)the larger will be the value of the chi-square statistic
B)the larger will be the critical value from the chi‐square distribution
C)the smaller will be the value of the chi-square statistic
D)the smaller will be the critical value from the chi‐square distribution

Question 73

When testing for equality of variances,the test statistic is obtained using the formula ________.

A) =
B)_{F =}
C)F =
D) =

Question 74

The chi-square test for independence is used to determine ________.

A)the degree to which there is a linear relationship between two variables
B)the difference between the means of two independent populations
C)whether the value of a population variance equals the hypothesized value
D)whether two categorical variables are independent

Question 75

The chi-square statistic has a chi-square distribution with ________ degrees of freedom.

A)n - 1
B)(n - 1)(n - 2)
C)(r - 1)(c - 1)
D)(r - 2)(c - 2)

Question 76

A weakness of ANOVA is that it ________.

A)does not work well for normally distributed variables
B)is not reliable when the outcome measures of the groups under study have equal variances
C)cannot determine which of the means are significantly different from the rest when the null hypothesis of the test is rejected
D)only works well with dichotomous factors and cannot evaluate differences within the factors if each factor has more than two possible levels

Question 77

ANOVA is a statistical technique that uses the ________.

A)distribution
B)t-distribution
C)chi-square distribution
D)Mann-Whitney distribution

Question 78

In one-sample tests for means,if the population standard deviation is unknown,then the sampling distribution of the mean is normal.

Question 79

The chi-square statistic is given by ________.

A) =
B) =
C) =
D) =

Question 80

The null hypothesis is based on new information provided by sample data.