Deck 7: Statistical Inference

Question 1

Which of the following propositions describes an existing theory or belief?

A) standard deviation
B) null hypothesis
C) proportion
D) alternative hypothesis

Answer 1

B

Question 2

Which of the following is true about determining the proper form of the hypotheses?

A) H0 is statistically proved true while testing
B) failure to reject H0 proves H1 wrong
C) H0 is always assumed to be true in testing
D) H1 is always assumed to be true in testing

Answer 2

C

Question 3

Which of the following is a valid one-sample hypothesis test?

A) H0: population parameter ≠ constant vs. H1: population parameter = constant
B) H0: population parameter > constant vs. H1: population parameter ≤ constant
C) H0: population parameter < constant vs. H1: population parameter ≥ constant
D) H0: population parameter = constant vs. H1: population parameter ≠ constant

Answer 3

D

Question 4

Use the data given below to answer the following question(s).
In a lower one-tailed hypothesis test, chosen level of significance = 0.10, sample size = 55, and t- test statistic = -1.76.
Which of the following is the conclusion?

A) This is a high probability and the conclusion is difficult.
B) The null hypothesis is rejected.
C) There are many sampling errors.
D) The null hypothesis cannot be rejected.

Question 5

Which of the following is the initial step in conducting a hypothesis test?

A) collecting data and calculating a test statistic
B) selecting a level of significance
C) identifying the population parameter of interest
D) determining a decision rule

Question 6

Use the data given below to answer the following question(s).
In a lower one-tailed hypothesis test, chosen level of significance = 0.10, sample size = 55, and t- test statistic = -1.76.
What is the observed level of significance?

A) 0.4605
B) 0.4191
C) 0.0379
D) 0.0420

Question 7

State how to increase the power of a test.
Compare and contrast the major types of hypothesis testing for one-sample tests
For a one-tailed test, the critical value:

A) divides the sampling distribution into three parts.
B) is the number of standard errors away from the sample mean.
C) helps determine if the test statistic falls in the rejection region or not.
D) fails to reject the null hypothesis if the test statistic exceeds the critical value.

Question 8

Which of the following denotes the power of the test?

A) α
B) 1 - β
C) β
D) 1 - α

Question 9

State how to increase the power of a test.
Compare and contrast the major types of hypothesis testing for one-sample tests
Which of the following is true about the rejection region?

A) The rejection region is chosen to determine the probability of a Type I error.
B) With a true null hypothesis, the test statistic falls into the rejection region.
C) If the test statistic is in the nonrejection region, the null hypothesis is rejected.
D) The rejection region occurs in the tails of the sampling distribution of the test statistic.

Question 10

Robin Inc. feared that the average company loss is running beyond $34,000. It initially conducted a hypothesis test on a sample extracted from its database. The hypothesis was formulated as H0: average company loss $34,000 vs. H1: average company loss > $34,000. The test resulted in favor of Robin Inc.'s loss not exceeding $34,000. Detailed study of company accounts later revealed that the average company loss had run up to $37,896. Which of the following errors were made during the hypothesis test?

A) Type III error
B) Type II error
C) Type I error
D) Type IV error

Question 11

Which of the following is true about the value of the power of the test?

A) low value will enable valid conclusions to be made
B) small sample sizes generate a low value of the power of the test
C) low value will help in detecting small differences in sample statistics
D) small sample sizes incur higher costs than large sample sizes

Question 12

The confidence coefficient is denoted by:

A) α
B) 1 - β
C) β
D) 1 - α

Question 13

A manufacturer wishes to determine if the average profit from the sale of his product exceeds $6,710. Which of the following is the appropriate hypothesis test?

A) H0: population mean profit from sale > $6,710 vs. H1: population mean profit from sale ≤ $6,710
B) H0: population mean profit from sale ≤ $6,710 vs. H1: population mean profit from sale > $6,710
C) H0: population mean profit from sale < $6,710 vs. H1: population mean profit from sale ≥ $6,710
D) H0: population mean profit from sale ≥ $6,710 vs. H1: population mean profit from sale < $6,710

Question 14

Which of the following probabilities gives the confidence coefficient?

A) P(rejecting H0 | H0 is true)
B) P(not rejecting H0 | H0 is false)
C) P(rejecting H0 | H0 is false)
D) P(not rejecting H0 | H0 is true)

Question 15

Type II error occurs when the test:

A) correctly fails to reject an actually true null hypothesis.
B) incorrectly fails to reject an actually false null hypothesis.
C) correctly rejects an actually false null hypothesis.
D) incorrectly rejects an actually true null hypothesis.

Question 16

What is the confidence coefficient when the level of significance is 0.03?

A) 0.9700
B) 0.0376
C) 0.7924
D) 0.7776

Question 17

Identify the power of the test from the following probabilities.

A) P(rejecting H0 | H0 is true)
B) P(not rejecting H0 | H0 is false)
C) P(rejecting H0 | H0 is false)
D) P(not rejecting H0 | H0 is true)

Question 18

Level of significance is the probability of:

A) incorrectly rejecting an actually true null hypothesis.
B) correctly failing to reject an actually true null hypothesis.
C) incorrectly failing to reject an actually false null hypothesis.
D) correctly rejecting an actually false null hypothesis.

Question 19

State how to increase the power of a test.
Compare and contrast the major types of hypothesis testing for one-sample tests

-The average cost for the sample of 5 sales of a product is $\begin{array}{|l|l|l|}\hline \text { Respondent } & \text { Gender } & \text { Breakfast Preference } \\\hline 1 & \text { Female } & \text { Fruits } \\\hline 2 & \text { Male } & \text { Cereal } \\\hline 3 & \text { Male } & \text { Milk } \\\hline 4 & \text { Female } & \text { Fruits } \\\hline 5 & \text { Female } & \text { Milk } \\\hline 6 & \text { Male } & \text { Cereal } \\\hline 7 & \text { Male } & \text { Milk } \\\hline 8 & \text { Male } & \text { Milk } \\\hline 9 & \text { Female } & \text { Fruits } \\\hline 10 & \text { Male } & \text { Fruits } \\\hline 11 & \text { Male } & \text { Cereal } \\\hline 12 & \text { Female } & \text { Cereal } \\\hline 13 & \text { Female } & \text { Milk } \\\hline 14 & \text { Male } & \text { Fruits } \\\hline 15 & \text { Female } & \text { Fruits } \\\hline\end{array}$ = $230 and the sample standard deviation is s = $17.50. The hypothesized mean is ?0 = $250. Compute the value of the test statistic.

A) -2.56
B) -4.00
C) -1.67
D) -3.87

Question 20

Explain how to draw a conclusion for one- and two-tailed hypothesis tests. LO2: Compare and contrast the major types of hypothesis testing for one-sample tests
Which of the following is true about one-tailed and two-tailed tests?

A) For standard normal and t-distributions, which have a mean of zero, lower-tail critical values are negative and upper-tail critical values are positive.
B) For an upper one-tailed test, if the test statistic is greater than the critical value, the decision would be to fail to reject the null hypothesis.
C) For a lower one-tailed test, if the test statistic is less than the critical value, the decision would be to fail to reject the null hypothesis.
D) For a two-tailed test, if the test statistic is either greater than the upper critical value or less than the lower critical value, the decision would be to fail to reject the null hypothesis.

Question 21

Use p-values to draw conclusions about hypothesis tests.
On studying the database, the manufacturer found out that the average difference between the estimated and actual total costs was $394. Based on the sample data, can the manufacturer conclude that the average difference between the estimated and actual total costs is different from zero?

Question 22

State the proper forms of hypotheses for two-sample hypothesis tests.
For a two-sample hypothesis test for differences in population parameters (1) and (2), which of the following is the correct form of an upper-tailed test?

A) H0: population parameter (1) - population parameter (2) ≥ 0 vs. H1: population parameter (1) - population parameter (2) < 0
B) H0: population parameter (1) - population parameter (2) > 0 vs. H1: population parameter (1) - population parameter (2) ≤ 0
C) H0: population parameter (1) - population parameter (2) < 0 vs. H1: population parameter (1) - population parameter (2) > 0
D) H0: population parameter (1) - population parameter (2) ≤ 0 vs. H1: population parameter (1) - population parameter (2) > 0

Question 23

Which of the following is true while applying the Excel ANOVA tool?

A) The specified input range of data must be separated.
B) The sample size for each factor level must be the same.
C) The input range must be a rectangular region that contains all data.
D) Level of significance need not be specified.

Question 24

If the alternative hypothesis includes the symbol <, the rejection region is in the upper tail.

Question 25

Use the data given below to answer the following question(s).
In a lower one-tailed hypothesis test, chosen level of significance = 0.10, sample size = 55, and t- test statistic = -1.76.
For a two-sample hypothesis which tests for differences in population parameters (1) and (2), a two-tailed test seeks evidence that population parameter:

A) seeks evidence that population parameter (2) is larger than parameter (1).
B) seeks evidence that population parameter (2) is the same as parameter (1).
C) seeks evidence that population parameter (2) is smaller than parameter (1).
D) seeks evidence that population parameters (1) and (2) do not belong to the same data.

Question 26

Which of the following 2010 Excel functions computes the p-value for the chi-square test?

A) CHISQ.INV.RT
B) CHIDIST
C) CHI.SQ
D) CHISQ.TEST

Question 27

State the proper forms of hypotheses for two-sample hypothesis tests.
For a lower-tail test, the p-value in the output from an Excel tool:

A) is correct if the test-statistic is negative.
B) is the difference from 1.0 if the test-statistic is negative.
C) is correct if the test-statistic is zero.
D) is correct if the test-statistic is positive.

Question 28

In order to reject the null hypothesis, the F-test statistic must be greater than the .

A) p-value
B) variance
C) df
D) F crit

Question 29

Which of the following is true about chi-square distribution?

A) It is a special distribution and is denoted by (C²).
B) It is characterized by degrees of freedom.
C) It is computed using the Excel function CHISQ.INV.TEST.
D) It has a left-tail area equal to the expected value of the sample.

Question 30

For a two-sample test for means with the population variance being known, the Excel procedure used is the Excel z-test.

Question 31

State the proper forms of hypotheses for two-sample hypothesis tests.
In a two-sample test for differences in means, the hypotheses are of the form:

Question 32

State the proper forms of hypotheses for two-sample hypothesis tests. Select and use Excel Analysis Toolpak procedures for two-sample hypothesis tests.
In conducting a hypothesis test, what is usually to be proven statistically is identified as the null hypothesis.

Question 33

State the proper forms of hypotheses for two-sample hypothesis tests.
Which of the following Excel tools is used for a two-sample test for equality of variances?

A) Excel F-test Two-sample for variances
B) Excel z-test: Two-sample for means
C) Excel t-test: Two-sample assuming unequal variances
D) Excel t-test: Two-sample assuming equal variances

Question 34

Which of the following tests is used to determine if two categorical variables are independent?

A) Chi-square test
B) t-test
C) z-test
D) ANOVA

Question 35

Conduct and interpret the results of a chi-square test for independence.
Use the data given below to answer the following question(s).
The following extract from a manufacturer's database shows a sample of 10 suppliers, their transportation charges, and the estimated and actual total costs of supplying materials. (Note: Assume a significance level of 0.05 wherever necessary.)
Conduct the appropriate type of one-sample test-statistic to determine whether the average transportation charge is less than $430.

Question 36

Conduct and interpret the results of a chi-square test for independence.
Use the data given below to answer the following question(s).
The following extract from a manufacturer's database shows a sample of 10 suppliers, their transportation charges, and the estimated and actual total costs of supplying materials. (Note: Assume a significance level of 0.05 wherever necessary.)
Conduct the appropriate type of one-sample test-statistic to determine whether the average transportation charge is less than $430. Apply a decision rule using the observed level of significance and draw a conclusion.

Question 37

Use the data given below to answer the following question(s).
In a lower one-tailed hypothesis test, chosen level of significance = 0.10, sample size = 55, and t- test statistic = -1.76.
Which of the following computes the test statistic for a one-sample test for proportions?