Deck 7: Statistical Inference

Question 1

Which of the following denotes the power of the test?

A) α
B) 1 - β
C) β
D) 1 - α

Answer 1

1 - β

Question 2

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

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

Answer 2

null hypothesis

Question 3

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

Answer 3

H0: population mean profit from sale ≤ $6,710 vs. H1: population mean profit from sale > $6,710

Question 4

Identify the power of the test from the following probabilities.

A) Prejecting H0 | H0 is true)
B) Pnot rejecting H0 | H0 is false)
C) Prejecting H0 | H0 is false)
D) Pnot rejecting H0 | H0 is true)

Question 5

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 6

The average cost for the sample of 5 sales of a product is $\bar x$ = $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 7

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 8

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 9

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 10

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 11

The confidence coefficient is denoted by:

A) α
B) 1 - β
C) β
D) 1 - α

Question 12

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

Question 13

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 14

Which of the following probabilities gives the confidence coefficient?

A) Prejecting H0 | H0 is true)
B) Pnot rejecting H0 | H0 is false)
C) Prejecting H0 | H0 is false)
D) Pnot rejecting H0 | H0 is true)

Question 15

Use the data given below to answer the following questions).
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 16

Which of the following is a Type I error?

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

Question 17

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

Question 18

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 19

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 20

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 21

Which of the following 2016 Excel functions computes the p-value for the chi-square test?

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

Question 22

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 23

In a two-sample test for means with the population variance being known, the z-test uses a test statistic that is based on the standard normal distribution.

Question 24

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 25

In conducting a hypothesis test, what is usually to be proven statistically is identified as the null hypothesis.

Question 26

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

Question 27

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 28

Use the data given below to answer the following questions).
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 29

Use the data given below to answer the following questions).
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.)
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 30

Use the data given below to answer the following questions).
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 31

Using the following data, test for the independence of the variables. Note: Assume a significance level of 0.05 wherever necessary.)

Question 32

During a study, individuals were asked to rate a product on a scale of 1-5. From the following data, help the researcher determine whether any significant differences exist in opinions among individuals from different regions. Note: Assume a significance level of 0.05 wherever necessary.)

Question 33

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 34

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 35

For a two-sample hypothesis which tests for differences in population parameters 1) and 2), a two-tailed test seeks evidence that:

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

Question 36

In statistical terminology, the variable of interest is called a .

A) critical value
B) p-value
C) factor
D) test-statistic

Question 37

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 38

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

Question 39

Use the data given below to answer the following questions).
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 40

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 41

Explain the assumptions underlying ANOVA along with their violations.

Question 42

How do test statistics for two-sample tests vary depending on whether the population standard deviations are known, and if not, whether they are assumed to be equal?

Question 43

For a two-sample test, explain the procedure used when it is difficult to justify the assumption that the variances of each population are equal.

Question 44

Why is testing for independence important for businesses?

Question 45

The first step in a chi-square test is to compute the observed frequency between each cell of the cross-tabulation if the two variables are independent.

Question 46

What are the four different outcomes of hypothesis testing?