BNAD Multiple Choice Questions
What are the degrees of freedom for the Jarque-Bera goodness-of-fit test for normality?
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
A demographer wants to measure life expectancy in countries 1 and 2. Let u1 and u2 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.) Ho: u1-u2<10 Ha: u1-u2>10
Using either the critical value approach or p-value approach, the decision and conclusion from above are _________________________________.
A.) do not reject the null hypothesis; we cannot conclude that not all of the proportions are equal to 0.25
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
Tukey's (HSD) method ensures that the probability of a Type I error remains fixed irrespective of the number of ________________.
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
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
Suppose you want to determine if gender and major are dependent. Which of the following tests should you use?
B.) Chi-square test for independence
Which of the following is the correct alternative hypothesis for the Jarque-Bera test for normality?
B.) Ha: the data is NOT normally distributed
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?
B.) Independent sampling with quantitative data
When calculating the santard error of x1-x2, under what assumption do you pool the sample variances s1 and s2?
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 observations 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?
B.) Zstat=2.4736
For the goodness-of-fit test, the sum of the expected frequencies must equal ___.
B.) n
When using Fisher's LSD method at some stated significance level, the probability of rejecting the null hypothesis when you should not increases as the number of _________________________.
B.) pairwise comparisons increases
The chi-square test of independence is a test of independence for __________________.
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 ______.
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 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?
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?
C.) A matched-pairs hypothesis test for uD
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?
C.) A t test under dependent or matched-pairs sampling.
The chi-square test of independence is only valid when the expected cell frequencies are _______________.
C.) at least 5
For the goodness-of-fit test, the chi-square test statistic will ________
C.) be greater than or equal to zero
The calculation of the Jarque-Bera test statistic involves___________.
C.) the sample size, skewness, and kurtosis
Which of the following null hypotheses is used to test if five population proportions are the same?
D. H0: p1=p2=p3=p4=p5=0.20
If there five treatments in a study, the number of pairwise comparisons need to compare all of the treatments is _______.
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?
D.) 60
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 μ1 and 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?
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 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.) H0: u1-u2>0 , Ha:u1-u2<0
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?
D.) H0:pa-p2<0, Ha:p1-p2>0
f 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?
D.) We cannot conclude that the data are not normally distributed
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 is greater than or equal to 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
40-44
Graph needed
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 chi- square distribution with two degrees of freedom.
TRUE
In the case when α1 and α2 are unknown and can be assumed equal, we need to calculate a pooled estimate of the variance to calculate the test statistic.
TRUE
The chi-square test statistic measures the difference between the observed frequencies and the expected frequencies assuming the null hypothesis is true.
TRUE
The difference between the two sample meand x1-x2 is an interval estimator of the difference between two population means u1-u2
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 α, the probability of rejecting the null hypothesis when you should not increase as the number of pairwise comparisons increases.
TRUE
Which of the following is the correct use of the Fisher's 100(1 - α)% confidence interval for μi - μj?
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.
54-58
graph needed
63-66
graph needed
16-21
table related
