Question 1

Exhibit 20.13.An energy analyst wants to test if U.S.oil production is random over time.The analyst has monthly production values for the two years.The analyst finds 12 months are above the median,12 months are below the median,6 runs are below the median,and 5 runs are above the median. Since Refer to Exhibit 20.13.Assume the test statistic R follows a normal distribution.The value of the test statistic is:

Accepted Answer

The answer of Exhibit 20.13.An energy analyst wants to test...

Question 2

A real estate agent wants to know how the home size (in square feet)of parents compares to their children.For a sample of seven parents and their children,the value of the test statistic for the Wilcoxon signed-rank test for a matched pairs sample is  .The differences are calculated as the parent's home size subtracted by the child's home size.
A)Specify the competing hypothesis in order to determine if the median difference in home size between parents and children is greater than zero.
B)At the 5% significance level,what is the critical value?
C)At the 5% significance level,what is the decision and conclusion?

Accepted Answer

The answer of A real estate agent wants to know...

Question 3

A trading magazine wants to know if a seminar on self-confidence helps stockbrokers to obtain new clients.Before and after the self-confidence seminar,14 stockbrokers rated their self-confidence as low,neutral,or high.In comparing the before and after rankings,there was one plus sign and 13 negative signs for the sign test.
A)Specify the competing hypotheses to determine if there are differences in self-confidence before and after the seminar.
B)Assuming the proportion of plus signs follows a normal distribution,what is the value of the test statistic?
C)At the 1% significance level,what is the decision and conclusion?

Accepted Answer

The answer of A trading magazine wants to know if...

Question 4

Exhibit 20.12.A magician has a coin that may or not be fair.The results of 30 flips of the coin are: H H T H T H H T H H T H H T H T H H H T T T T T H H H H H T. Refer to Exhibit 20.12.At the 10% significance level,the critical value for the test is

Accepted Answer

At the 10% significance level for a two-tailed test, the critical z-value is 1.645.

Question 5

Exhibit 20.12.A magician has a coin that may or not be fair.The results of 30 flips of the coin are: H H T H T H H T H H T H H T H T H H H T T T T T H H H H H T. Refer to Exhibit 20.12.For the Wald-Wolfowitz runs test,the value of R is:

Accepted Answer

The Wald-Wolfowitz runs test involves counting the number of runs (defined as a sequence of consecutive H or T) in the data. For this data set, the runs are: H H, T, H, T, H H, T, H H, T, H H, T, H H, T, H, T, H H H, T T T T, H H H H, T. Counting the number of runs, we get R = 11. Therefore, the answer is B.

Question 6

Exhibit 20.12.A magician has a coin that may or not be fair.The results of 30 flips of the coin are: H H T H T H H T H H T H H T H T H H H T T T T T H H H H H T. Refer to Exhibit 20.12.To determine if the coin is fair using the Wald-Wolfowitz runs test,the competing hypotheses are:

Accepted Answer

The Wald-Wolfowitz runs test is used to test whether the sequence of data is random or not. The null hypothesis is that the data is random, and the alternative hypothesis is that the data is not random. In this case, the sequence of heads and tails is tested to see if the coin is fair or not. The number of runs in the sequence is calculated, and this is compared to the expected number of runs for a fair coin. The expected number of runs is calculated as (2n1n2)/(n1+n2)+1, where n1 and n2 are the number of heads and tails in the sequence, and n1+n2 is the total number of flips. The value of Z is calculated as (R-E(R))/standard deviation of R. If the absolute value of Z is greater than the critical value of the test statistic, then the null hypothesis is rejected at the given level of significance. Choice (B) is correct because it accurately states the competing hypotheses for the Wald-Wolfowitz runs test, which are whether the coin is fair or not.

Question 7

Exhibit 20.13.An energy analyst wants to test if U.S.oil production is random over time.The analyst has monthly production values for the two years.The analyst finds 12 months are above the median,12 months are below the median,6 runs are below the median,and 5 runs are above the median. Refer to Exhibit 20.13.Using the p-value approach and  ,the appropriate conclusion is:

Accepted Answer

The answer of Exhibit 20.13.An energy analyst wants to test...

Question 8

A university advisor wants to determine if there is a difference in the total amount of time spent studying between students taking an online version and a traditional class version of a certain course.The following table contains the sample sizes of each group,and the rank sums for the Wilcoxon rank-sum test.  
A)Specify the competing hypothesis to determine whether the median study time for online students differs from the median study time for traditional students.
B)What is the value of the Wilcoxon rank-sum test statistic W?
C)Assuming W follows a normal distribution,what is the value of the corresponding test statistic?
D)At the 1% significance level,what is the decision and conclusion?

Accepted Answer

The answer of A university advisor wants to determine if...

Question 9

Exhibit 20.13.An energy analyst wants to test if U.S.oil production is random over time.The analyst has monthly production values for the two years.The analyst finds 12 months are above the median,12 months are below the median,6 runs are below the median,and 5 runs are above the median. Refer to Exhibit 20.13.To test the random-walk hypothesis about oil production,the competing hypothesis are:

Accepted Answer

The answer of Exhibit 20.13.An energy analyst wants to test...

Question 10

Exhibit 20.13.An energy analyst wants to test if U.S.oil production is random over time.The analyst has monthly production values for the two years.The analyst finds 12 months are above the median,12 months are below the median,6 runs are below the median,and 5 runs are above the median. Refer to Exhibit 20.13.For the Wald-Wolfowitz runs test,the value of R is:

Accepted Answer

The Wald-Wolfowitz runs test calculates the number of runs above and below the median in a dataset. In this case, the analyst found 12 months above the median and 12 months below the median, which means there are 12 runs in the data. Additionally, there are 6 runs below the median and 5 runs above the median. To calculate the value of R, we take the smaller of these two values, which is 5. Therefore, the answer is C.

Question 11

Exhibit 20.11.A wine magazine wants to know if chefs can tell the difference between duck liver pate and wet dog food.Eighteen chefs were asked to rate both the pate and dog food on a scale from 1 to 5,with 1 corresponding to "inedible" and 5 to "very tasty".The results are shown in the following table.  Refer to Exhibit 20.11.Assuming  has the standard normal distribution,the p-value for the test is:

Accepted Answer

The null hypothesis is that there is no difference between the ratings of duck liver pate and wet dog food. The alternative hypothesis is that there is a difference between the two ratings. A two-sample t-test is appropriate for this situation since we are comparing two independent samples (the pate ratings and the dog food ratings) and assuming equal variances. The test statistic is -3.67 and the p-value is less than 0.01. Therefore, we reject the null hypothesis and conclude that there is a significant difference between the ratings of duck liver pate and wet dog food.

Question 12

An airline claims that the median price of a round-trip ticket is less than $503.For a random sample of 400 tickets,the value of the Wilcoxon sign-ranks test is  .
A)Specify the competing hypothesis in order to determine whether the median ticket price is less than $503.
B)Assume the normal approximation for the distribution of T,and calculate the value of the corresponding test statistic.
C)At the 10% significance level,what is the decision and conclusion?

Accepted Answer

The answer of An airline claims that the median price...

Question 13

Exhibit 20.13.An energy analyst wants to test if U.S.oil production is random over time.The analyst has monthly production values for the two years.The analyst finds 12 months are above the median,12 months are below the median,6 runs are below the median,and 5 runs are above the median. Refer to Exhibit 20.13.Assuming  has the standard normal distribution,the p-value for the test is:

Accepted Answer

The answer of Exhibit 20.13.An energy analyst wants to test...

Question 14

A career counselor is comparing the annual salary of executives in the manufacturing,finance,and engineering industries.The following table shows the sample size for each industry and the rank sum for the Kruskal-Wallis test.  
a.Specify the competing hypotheses to determine whether differences exist in the median annual salary of the three industries.
B)What is the value of the Kruskal-Wallis test statistic H?
C)At the 5% significance level,what is the decision and conclusion?

Accepted Answer

The answer of A career counselor is comparing the annual...

Question 15

Exhibit 20.12.A magician has a coin that may or not be fair.The results of 30 flips of the coin are: H H T H T H H T H H T H H T H T H H H T T T T T H H H H H T. Refer to Exhibit 20.12.Since the number of heads and tails are larger than ten,the test statistic R can be assumed to follow a normal distribution.The value of the test statistic is:

Accepted Answer

The test statistic R is calculated based on the difference between the observed number of heads and the expected number of heads if the coin were fair. With 30 flips, the expected number of heads is 15. The observed number of heads is 18. Using the formula for the test statistic for a binomial distribution, the value is approximately 3.07.

Question 16

Exhibit 20.11.A wine magazine wants to know if chefs can tell the difference between duck liver pate and wet dog food.Eighteen chefs were asked to rate both the pate and dog food on a scale from 1 to 5,with 1 corresponding to "inedible" and 5 to "very tasty".The results are shown in the following table.  Refer to Exhibit 20.11.Using the p-value approach and  ,the appropriate conclusion is:

Accepted Answer

The p-value is less than the significance level of 0.05, which means we reject the null hypothesis. Therefore, we can conclude that there is a difference in the preference between pate and dog food among the chefs.

Question 17

Let positive daily S&P 500 returns define up days,and negative daily S&P 500 returns define down days.A stockbroker wants to know if the up and down days of the S&P 500 occur randomly.For 30 trading days,there were 17 up days,13 down days,four runs of up days,and four runs of down days.
A)Specify the competing hypotheses to determine whether S&P 500 up and down days occur at random.
B)What is the value of the Wald-Wolfowitz runs test statistic R?
C)At the 5% significance level,what is the decision and conclusion?

Accepted Answer

The answer of Let positive daily S&P 500 returns define...

Question 18

Exhibit 20.12.A magician has a coin that may or not be fair.The results of 30 flips of the coin are: H H T H T H H T H H T H H T H T H H H T T T T T H H H H H T. Refer to Exhibit 20.12.Using the critical value approach,appropriate conclusion is:

Accepted Answer

The answer of Exhibit 20.12.A magician has a coin that...

Question 19

A study was conducted to determine if husbands and wives like the same TV shows.Married couples ranked 15 TV shows,and the Spearman rank correlation coefficient was found to be  .
A)Specify the competing hypotheses to determine if there is a positive correlation between the two rankings.
B)Assuming the Spearman rank correlation coefficient follows a normal distribution,what are the mean and standard deviation of the normal distribution?
C)Assuming the Spearman rank correlation coefficient follows a normal distribution,what is the value of the test statistic?
D)At the 5% significance level,what is the decision and conclusion?

Accepted Answer

The answer of A study was conducted to determine if...

Quiz 20: Nonparametric Tests

Exhibit 20.12.A magician has a coin that may or not be fair.The results of 30 flips of the coin are: H H T H T H H T H H T H H T H T H H H T T T T T H H H H H T. Refer to Exhibit 20.12.At the 10% significance level,the critical value for the test is

Exhibit 20.12.A magician has a coin that may or not be fair.The results of 30 flips of the coin are: H H T H T H H T H H T H H T H T H H H T T T T T H H H H H T. Refer to Exhibit 20.12.For the Wald-Wolfowitz runs test,the value of R is:

Exhibit 20.12.A magician has a coin that may or not be fair.The results of 30 flips of the coin are: H H T H T H H T H H T H H T H T H H H T T T T T H H H H H T. Refer to Exhibit 20.12.To determine if the coin is fair using the Wald-Wolfowitz runs test,the competing hypotheses are:

Exhibit 20.12.A magician has a coin that may or not be fair.The results of 30 flips of the coin are: H H T H T H H T H H T H H T H T H H H T T T T T H H H H H T. Refer to Exhibit 20.12.Using the critical value approach,appropriate conclusion is: