BNAD 277

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. Independent sampling with quantitative data

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

False

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

False

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.

False

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

False

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

False

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

False

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

False

. The difference between the two sample means 𝑿̅𝟏 − 𝑿̅𝟐 is an interval estimator of the difference between two population means 𝝁𝟏 − 𝝁𝟐

True

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

True

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

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

True

In the case when 𝝈𝟏/2 and 𝝈𝟐/2 are unknown and can be assumed equal, we can calculate a pooled estimate of the variance.

True

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

True

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

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

True

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. 2

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. Conclude that the mean attendance differs

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. H0: 𝜇1 - 𝜇2 ≤ 10, HA: 𝜇1 - 𝜇2 > 10

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. goodness-of-fit test for a multinomial experiment

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. pairwise comparisons

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. reject the null hypothesis of equal population means

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. the population variances are known

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. the row total multiplied by the column total divided by the sample size

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

b. 2

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. Chi-square test for independence

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. HA: the data is NOT normally distributed

When calculating the standard error of 𝑿̅𝟏 − 𝑿̅𝟐 , under what assumption do you pool the sample variances 𝒔𝟏/𝟐 and 𝒔𝟐/𝟐? 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. Unknown population variances that are assumed equal.

A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening. Two independent samples of 25 weeks are collected for Tuesday and Wednesday. The mean attendance on Tuesday evening is calculated as 5,500, while the mean attendance on Wednesday evening is calculated as 5,850. The known population standard deviation for attendance on Tuesday evening is 550 and the known population standard deviation for attendance on Wednesday evening is 445. Which of the following is the absolute value of the appropriate test statistic? a. Zstat = 55.479 b. Zstat = 2.4736 c. tstat = 55.479 d. tstat = 2.4736

b. Zstat = 2.4736

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. pairwise comparisons increases

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. two qualitative variables

The heights (in cm) for a random sample of 60 male employees of S&M Construction Company were measured. The sample mean is 166.5, the standard deviation is 12.57, the sample kurtosis is 0.12, and the sample skewness is −0.23. The value of the Jarque-Bera test statistic is ______. a. 0.28 b. −0.493 c. 0.57 d. 2

c. 0.57

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 instate applicants and 35 out-of-state applicants. The mean SAT math score for instate 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. 68

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. A matched-pairs hypothesis test for 𝜇D

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. A t test under dependent or matched-pairs sampling

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. at least 5

For the goodness-of-fit test, the chi-square test statistic will __________________. a. always equal zero b. always be negative c. be greater than or equal to zero d. always be equal to n

c. be greater than or equal to zero

If units within each block are randomly assigned to each of the treatments, then the design of the experiment is referred to as a _______________________. a. factorial design b. completely randomized design c. randomized block design d. balanced incomplete block design

c. randomized block design

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 d. the sample average, skewness, and kurtosis

c. the sample size, skewness, and kurtosis

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

d. 10

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. 60

A farmer uses a lot of fertilizer to grow his crops. The farmer's manager thinks fertilizer products from distributor A contain more of the nitrogen that his plants need than distributor B's fertilizer does. He takes two independent samples of four batches of fertilizer from each distributor and measures the amount of nitrogen in each batch. Fertilizer from distributor A contained an average of 23 pounds per batch and fertilizer from distributor B contained an average of 18 pounds per batch. Suppose the population standard deviation for distributor A and distributor B is four pounds per batch and five pounds per batch, respectively. Assume the distribution of nitrogen in fertilizer is normally distributed. Let µ1and µ2 represent the average amount of nitrogen per batch for fertilizer's A and B, respectively. Which of the following is the appropriate conclusion at the 5% significance level? a. Reject H0; we can conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B. b. Reject H0; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B. c. Fail to reject H0; we can conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B. d. Fail to reject H0; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.

d. Fail to reject H0; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.

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. H0: p1 = p2 = p3 = p4 = p5 = 0.20

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. H0: 𝑝1 - 𝑝2 ≤ 0, HA: 𝑝1 - 𝑝2 > 0

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? a. H0: 𝜇𝐷 ≤ 0, HA: 𝜇𝐷 > 0 b. H0: 𝜇𝐷 ≥ 0, HA:𝜇𝐷 < 0 c. H0: 𝜇1 - 𝜇2 ≤ 0, HA: 𝜇1 - 𝜇2 > 0 d. H0: 𝜇1 - 𝜇2 ≥ 0, HA: 𝜇1 - 𝜇2 < 0

d. H0: 𝜇1 - 𝜇2 ≥ 0, HA: 𝜇1 - 𝜇2 < 0

Which of the following is the correct interpretation of the Fisher's 100(1 - α)% confidence interval for μi - μj? a. If the interval includes the value zero, the null hypothesis, that H0: μi - μj = 0, is rejected for the α level of significance. b. If the interval includes the value zero, the null hypothesis, that H0: μi - μj = 0, is rejected for the 100(1 - α)% level of significance. c. If the interval does not include the value zero, the null hypothesis, that H0: μi - μj = 0, is rejected at 100(1 - α)% level of significance. d. If the interval does not include the value zero, the null hypothesis, that H0: μi - μj = 0, is rejected at α level of significance.

d. If the interval does not include the value zero, the null hypothesis, that H0: μi - μj = 0, is rejected at α level of significance.

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. May assume any value

If you do a Jarque-Bera test for normality and fail to reject the null hypothesis, which of the following would be the correct interpretation of your findings? a. We can conclude that the data are normally distributed b. We cannot conclude that the data are normally distributed c. We can conclude that data are not normally distributed d. We cannot conclude that the data are not normally distributed

d. We cannot conclude that the data are not normally distributed

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

b. n