Deck 15: Nonparametric Inference

Question 1

Using Appendix B, Table 7, find:

C) The point c such that is close to 0.03 when n_A = 8, n_B = 9.

Answer 1

Part A: 0.033
Part B: 0.074
Part C: 92

Question 2

Using Appendix B, Table 7, find the points c₁ and c₂ such that
is about 0.026 when n_A = 6, n_B = 7. Provide your answer in the form (c₁, c₂).

A) (29, 55)
B) (56, 28)
C) (27, 57)
D) (26, 58)

Answer 2

(56, 28)

Question 3

Independent samples of size n_A = 3 and n_B = 3 are taken from two continuous populations.

A) How many possible collections of ranks associated with population A are there?
B) Obtain the null distribution of W_A.

Answer 3

Part A: 20

Question 4

A study about the concentration of mercury in the sediment of two lakes shows the following numbers.
Using the Wilcoxon rank-sum procedure, test if the mercury concentration is different for the two lakes. Use α = 0.05. Answer "Mercury concentration is (is not) significantly different for the two lakes".

Question 5

In some colleges, the Calculus course is taught in two different formats: in campus and on-line. The passing percents per section are shown below.
Do the data strongly indicate different passing percent's among the two teaching formats?

Question 6

The number of breathing pauses per hour(BPH) helps determine a sleeping disorder.
The values of BPH from a random sample of 5 males and a random sample of 5 females are

A) Test for equality using the Wilcoxon rank-sum test with approximately 0.05. Answer "The populations are identical" or "The populations are different".

B) Determine the significance probability.

Question 7

In a study of two treatment effects a sample of size 31 is taken. If in 7 pairs, the two responses are equal, then the sign test is performed with the effective sample size n = 24.

Question 8

Use Appendix B. Table 8, to find:

A)
B)
C) The value of c so that is nearly 0.05 when n = 13.

Question 9

A publicist group when testing the preferences, among the executives of a company, for the two formats of a TV commercial , discover that 12 out of 17 subjects favored format A. Using the sign test, find the significance probability when H₁ states that format A is preferable.

Question 10

The following data shows the recent population percents by gender.
Is there a difference between the population percents?

A) Use the sign test with α below 0.05.
B) Find the significance probability.

Question 11

The following data shows the recent population percents by gender.
Is there a difference between the population percents? Apply the Wilcoxon signed-rank test with .
α near 0.05.

Question 12

The number of goals in favor (G.F) and goals against (G.A) by the first four national teams in one year's F.I.F.A World Cup is shown below.
Calculate Spearman's rank correlation

Question 13

Use the one side test to determine the significance probability when
r_SP= 0.08 and n = 48. Round your answer to four decimal places.

Question 14

The mean bacteria count per unit volume of lake water is obtained from each sample of lake water. Five values are obtained from each to two beaches.

Evaluate Wilcoxon's rank-sum statistic based on the Beach 1.

Question 15

15 Each of two judges in a popular dancing contest assigns a score from 3 through 7 to each participating couple.

Conduct a signed rank test with the intent of showing that Judge 1 typically gives higher scores. Take α = .05.
[Hint: P [ T + ≥ 19 ] = .047.