BNAD 277: Conceptual Questions

. Using the scenario above, which of the following is the appropriate decision given a 5% level of significance? a. Conclude that the mean attendance differs b. Conclude that the mean attendance does not differs c. Cannot conclude that the mean attendance differs d. Cannot conclude that the mean attendance does not differs

A

30. If the amount of variability between treatments is significantly greater than the amount of variability within treatments, then _________. a. reject the null hypothesis of equal population means b. do not reject the null hypothesis of equal population means c. conclude that the ratio of between-treatments variability to within-treatments variability is significantly less than 1 d. perform further analysis using the two-way ANOVA with interaction

A

38. When testing the difference between two population means under independent sampling, we use the z distribution if _________ . a. the population variances are known b. the population variances are unknown, but assumed to be equal c. the population variances are unknown and cannot be assumed equal d. Both the population variances are known and the population variances are unknown, but assumed to be equal

A

40. Packaged candies have three different types of colors. Suppose you want to determine if the population proportion of each color is the same. The most appropriate test is the ______________________________________. a. goodness-of-fit test for a multinomial experiment b. chi-square test for independence c. goodness-of-fit test for normality d. Jarque-Bera test for normality

A

47. Using either the critical value approach or p-value approach, the decision and conclusion from above are _________________________________________. b. do not reject the null hypothesis; all of the population proportions are the same c. reject the null hypothesis; conclude that not all proportions are equal to 0.25 d. reject the null hypothesis; cannot conclude that not all proportions are equal to 0.25

A

49. Tukey's (HSD) method ensures that the probability of a Type I error remains fixed irrespective of the number of ________________. a. pairwise comparisons b. treatments c. replications within each treatment d. replications for each combination of factor A and factor B

A

52. For the chi-square test of independence, the expected cell frequencies are found as ________________. a. the row total multiplied by the column total divided by the sample size b. the observed cell frequency c. (r−1)(c−1) d. rc

A

53. What are the degrees of freedom for the Jarque-Bera goodness-of-fit test for normality? a. 2 b. k−3 c. k−2 d. k−1

A

57. To test that gender and candidate preference are independent, the null hypothesis is ___________________________. a. H0: Gender and candidate preference are independent b. H0: Gender and candidate preference are mutually exclusive c. H0: Gender and candidate preference are not mutually exclusive d. H0: Gender and candidate preference are dependent

A

58. Using above, for the chi-square test of independence, the assumed degrees of freedom are ____. a. 1 b. 2 c. 3 d. 4

A

61. Using either the critical value approach or p-value approach, the decision and conclusion are _________________________________________. a. reject the null hypothesis; gender and candidate preference are dependent b. do not reject the null hypothesis; gender and candidate preference are independent c. reject the null hypothesis; gender and candidate preference are independent d. do not reject the null hypothesis; gender and candidate preference are dependent

A

A demographer wants to measure life expectancy in countries 1 and 2. Let 𝝁𝟏 and 𝝁𝟐 denote the mean life expectancy in countries 1 and 2, respectively. Specify the hypothesis to determine if life expectancy in country 1 is more than 10 years higher than in country 2. a. H0: 𝜇1 - 𝜇2 ≤ 10, HA: 𝜇1 - 𝜇2 > 10 b. H0: 𝜇1 - 𝜇2 ≥ 10, HA: 𝜇1 - 𝜇2< 10 c. H0:𝜇1 -𝜇2<10,HA:𝜇1 -𝜇2 ≥ 10 d. H0:𝜇1 -𝜇2 = 10,HA:𝜇1 -𝜇2≠10

A

23. Suppose you want to perform a test to compare the mean GPA of all freshmen with the mean GPA of all sophomores in a college? What type of sampling is required for this test? a. Independent sampling with qualitative data b. Independent sampling with quantitative data c. Matched-pairs sampling with qualitative data d. Matched-pairs sampling with quantitative data

B

41. Suppose you want to determine if gender and major are dependent. Which of the following tests should you use? a. Goodness-of-fit test for a multinomial experiment b. Chi-square test for independence c. Goodness-of-fit test for normality d. Jarque-Bera test for normality

B

43. To test if the poker-dealing machine deals cards at random, the null and alternative hypotheses are ________________________________________. a. H0:p1 =p2 =p3 =p4 =0, HA: Not all population proportions are equal to 0,25 c. H0:p1 =p2 =p3 =p4 =1, HA: Not all population proportions are equal to 0,25 d. H0:p1 =p2 =p3 =p4 ==0.20, HA: Not all population proportions are equal to 0,20

B

44. Using the problem above, for the goodness-of-fit test, the degrees of freedom are ____. a. 2 b. 3 c. 4 d. 5

B

45. Using the problem above, for the goodness-of-fit test, the value of the test statistic is _____. a. 2.25 b. 3.125 c. 6.45 d. 7.815

B

46. Using the problem above, at the 5% significance level, the critical value is ______. a. 6.251 b. 7.815 c. 9.348 d. 11.345

B

54. Which of the following is the correct alternative hypothesis for the Jarque-Bera test for normality? a. HA: the data is normally distributed b. HA: the data is NOT normally distributed c. HA: Category A and Category B are dependent d. HA: Category A and Category B are independent

B

68. Assuming that race and seniority are independent, which of the following is the expected frequency of Asian directors? a. 0 b. 1.95 c. 3.91 d. 5.42

B

For the goodness-of-fit test, the sum of the expected frequencies must equal ___. a. 1 b. n c. k d. k−1

B

In a two-way ANOVA test, how many null hypotheses are tested? a. 1 b. 2 c. 3 d. More than 3

B

The chi-square test of independence is a test of independence for __________________. a. a single qualitative variable b. two qualitative variables c. two quantitative variables d. three or more quantitative variables

B

When using Fisher's LSD method at some stated significance level, the probability of committing a Type I error increases as the number of a. pairwise comparisons decreases b. pairwise comparisons increases c. sample size increases d. treatments decreases

B

̅̅ 32. When calculating the standard error of 𝑿𝟏 − 𝑿𝟐 , under what assumption do you pool the sample variances 𝒔𝟐 and 𝒔𝟐 ? 𝟏𝟐 a. Known population variances. b. Unknown population variances that are assumed equal. c. Unknown population variances that are assumed unequal. d. All of these choices are correct

B

42. A particular personal trainer works primarily with track and field athletes. She believes that her clients run faster after going through her program for six weeks. How might she test that claim? a. A hypothesis test for 𝜇1 - 𝜇2 . b. A hypothesis test for 𝑝1 - 𝑝2 c. A matched-pairs hypothesis test for 𝜇𝐷 d. We are unable to conduct a hypothesis test because the samples would not be independent.

C

48. The chi-square test of independence is valid when the expected cell frequencies are _______________. a. equal to 0 b. more than 0 but less than 5 c. at least 5 d. negative

C

50. What type of test for population means should be performed when examining a situation in which employees are first tested, then trained, and finally retested? a. A z test under independent sampling with known population variances. b. A t test under independent sampling with unknown but equal population variances. c. A t test under dependent or matched-pairs sampling. d. A t test under independent sampling with unknown and unequal population variances.

C

55. A university wants to compare out-of-state applicants' mean SAT math scores (μ1) to in-state applicants' mean SAT math scores (μ2). The university looks at 35 in- state applicants and 35 out-of-state applicants. The mean SAT math score for in- state applicants was 540, with a standard deviation of 20. The mean SAT math score for out-of-state applicants was 555, with a standard deviation of 25. It is reasonable to assume the corresponding population standard deviations are equal. To calculate the confidence interval for the difference μ1 - μ2, what is the number of degrees of freedom of the appropriate probability distribution? a. 64 b. 64.87 c. 68 d. 69

C

56. The calculation of the Jarque-Bera test statistic involves___________. a. the sample size, standard deviation, and kurtosis b. the sample size, standard deviation, and average c. the sample size, skewness, and kurtosis d. the sample average, skewness, and kurtosis

C

59. Using above, for the chi-square test of independence, the value of the test statistic is _______. a. 2.34 b. 1.62 c. 3.25 d. 4

C

69. For the chi-square test for independence, the degrees of freedom used are _____. a. 2 b. 16 c. 9 d. 8

C

39. If there are five treatments under study, the number of pairwise comparisons is _______. a. 15 b. 5 c. 20 d. 10

D

51. You would like to determine if there is a higher proportion of smoking among women than among men in a neighborhood. Let women and men be represented by populations 1 and 2, respectively. Which of the following hypotheses is relevant to this claim? a. H0: 𝜇1 -𝜇2 ≥ 0, HA: 𝜇1 - 𝜇2 < 0 b. H0: 𝜇1 -𝜇2 ≤ 0, HA: 𝜇1 - 𝜇2 > 0 c. H0: 𝜇1 -𝜇2 < 0, HA: 𝜇1 - 𝜇2 ≥ 0 d. H0: 𝑝1 -𝑝2 ≤ 0, HA: 𝑝1 - 𝑝2 > 0 e. H0: 𝑝1 -𝑝2 ≥ 0, HA: 𝑝1 - 𝑝2 < 0

D

60. Using above, At the 10% significance level, the critical value is _______. a. 6.635 b. 5.024 c. 3.841 d. 2.706

D

7. In the test for comparing two population means when population variances are unknown and unequal, a student calculates the degrees of freedom using the proper formula as 61.75. Per the t-table you were given, how many degrees of freedom should the student use to find the critical value or p-value of the test? a. 61 b. 61.75 c. 62 d. 60

D

When comparing two population means, their hypothesized difference _________ . a. must be negative b. must be positive c. must be zero d. may assume any value

D

Which of the following null hypotheses is used to test if five population proportions are the same? a. H0:p1 =p2 =p3 =p4 =p5 =0.25 b. H0:p1 =p2 =p3 =p4 =0.25 c. H0:p1 =p2 =p3 =p4 =0.20 d. H0:p1 =p2 =p3 =p4 =p5 =0.20

D

Which of the following pairs of hypotheses are used to test if the mean of the first population is smaller than the mean of the second population, using independent random sampling?

D

. The same formulas are used to compute the test statistic whether the hypothesized difference between population proportions is zero or not. True False

F

4. For a multinomial experiment with k categories, the goodness-of-fit test statistic is assumed to follow a chi-square distribution with k degrees of freedom. True False

F

A goodness-of-fit test analyzes two qualitative variables whereas a chi-square test of a contingency table is for a single qualitative variable. True False

F

ANOVA is a statistical technique used to determine if differences exist between the means of two populations. True False

F

If the underlying populations cannot be assumed to be normal, then by the central ̅̅ limit theorem, the sampling distribution of 𝑿𝟏 − 𝑿𝟐 is approximately normal only if the sum of the sample observations is sufficiently large—that is, when 𝒏𝟏 + 𝒏𝟐 ≥ 𝟑𝟎 True False

F

The t statistic is used to estimate the difference between two population proportions. True False

F

Two random samples are considered independent if the observations in the first sample are different from the observations of the second sample. True False

F

Decision Rule Test > Crit

Reject

Decision Rule: P < a

Reject

5. For a chi-square goodness-of-fit test, the expected category frequencies are calculated using the sample category proportions. True False

T

For a chi-square test of a contingency table, the degrees of freedom are calculated as (r−1)(c−1) where r and c are the number of rows and columns in the contingency table. True False

T

For the Jarque-Bera test for normality, the test statistic is assumed to have a chi- square distribution with two degrees of freedom. True False

T

In the case when 𝝈𝟐 and 𝝈𝟐 are unknown and can be assumed equal, we can calculate a pooled estimate of the variance. True False

T

The chi-square test statistic measures the difference between the observed frequencies and the expected frequencies assuming the null hypothesis is true. True False

T

We use ANOVA to test for differences between population means by examining the amount of variability between the samples relative to the amount of variability within the samples. True False

T

When using Fisher's least difference (LSD) method at some stated significance level α, the probability of committing a Type I error increases as the number of pairwise comparisons increases. True False

T

𝟏𝟐 True FalseThe difference between the two sample means 𝑿𝟏 − 𝑿𝟐 is an interval estimator of ̅̅ the difference between two population means 𝝁𝟏 − 𝝁𝟐 . True False

T