Two boxes are labelled I and II. Box I contains 4 black balls and 6 white balls. Box II contains 2 black balls and 8 white balls. A player randomly selects one box and then randomly draws 2 balls without replacement from the selected box.

1) What is the probability of obtaining 2 black balls?

2) Given that 2 black balls are obtained, what is the probability that Box I is selected?

3) Suppose that 20 players conduct the game independently. What is the probability that exactly 4 players obtain 2 black balls?

Use the median of 3 partitioning algorithm (given in the next page) to implement quick sort. This algorithm chooses the pivot element as the median of the 3 elements namely: A[p], A[r], and A[(p+r)/2].(Java language)

Quicksort(A,p,r)

1 if p

2 N = r- p +1

3 m = Median3(A, p, p + N/2 , r)

4 exchange A[m] with A[r]

5 q = Partition (A,p,r)

6 Quicksort(A,p, q-1)

7 Quicksort(A,q+1,r)

Software Testing Question

Program P2 CFG.

a) Identify the basic blocks for the following program P2 written in pseudo-code.

b) Draw the control flow graph.

Program P2

1) integer A, B;

2) input (A);

3) B = 1;

4) while (int i=1; i<=A; i++)

5) {

6) B = B * i;

7) if (B>13)

8) B = B / 2;

9) else 1

0) B = B * 2;

11) }

12) output (A,B);

13) end;

Bill Fennema, a president of Fennema Construction, has developed the tasks, durations, and predecessor relationships in the following table for building new motels. Draw the AOA network and answer the questions that follow.

Activity	Immediate Predecessor(s)	Time Estimates (in weeks)
		Optimistic	Most likely	Pessimistic
A	-	4	8	10
B	A	2	8	24
C	A	8	12	16
D	A	4	6	10
E	B	1	2	3
F	E, C	6	8	20
G	E, C	2	3	4
H	F	2	2	2
I	F	6	6	6
J	D, G, H	4	6	12
K	I, J	2	2	3

a) What is the variance for activity H?
b) What is the critical path for the project?
c) What is the estimated time of the critical path?
d) What is the probability that the project duration will not be less than 35 weeks?

A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows:

Salary			Education
	34			3
	66			1
	⋮			⋮
	33			0

Salary	Education
34	3
66	1
89	4
56	3
71	7
80	2
111	7
51	0
23	7
36	2
100	1
35	1
71	6
68	9
163	5
56	0
86	5
58	4
128	9
33	0

a. Find the sample regression equation for the model: Salary = β₀ + β₁Education + ε. (Round answers to 2 decimal places.)

Salaryˆ=Salary^=    +   Education

b. Interpret the coefficient for Education.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $8,590.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $4,690.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $4,690.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $8,590.

c. What is the predicted salary for an individual who completed 7 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.)

SalaryˆSalary^               $

You want to know if a nurse’s absences from work in one month (Y) are correlated with her score on a psychological test of burnout (X). Higher scores = more burnout. What conclusions do you draw from the data below?

Nurse   Burnout (X) Absences (Y)

1. 2 4

2 1 7

3 2 6

4 3 9

5 4 6

6 4 8

7 7 7

8 7 10

9 8 11

Please use SPSS to compute the test statistic for the following problems. For those questions, please turn in the appropriate SPSS output.

1. Perform the appropriate analysis
2. Wherever appropriate, calculate and report effect size(s)
3. Make a decision regarding the null hypothesis and write an APA-style conclusion interpreting your statistical results with regard to the aims of the experiment and as you would write it up in a report, including the statistical evidence to back it up.

Splish Company is a multi product firm. Presented below is information concerning one of its products, the Hawkeye.

Date		Transaction		Quantity		Price/Cost
1/1		Beginning inventory		2,000		$15
2/4		Purchase		3,000		23
2/20		Sale		3,500		38
4/2		Purchase		4,000		29
11/4		Sale		3,200		42

Average-cost per unit $ _______

Compute cost of goods sold, assuming Splish uses: (Round average cost per unit to 4 decimal places, e.g. 2.7631 and final answers to 0 decimal places, e.g. 6,548.) Cost of goods sold

(a) Periodic system, FIFO cost flow $

(b) Perpetual system, FIFO cost flow $

(c) Periodic system, LIFO cost flow $

(d) Perpetual system, LIFO cost flow $

(e) Periodic system, weighted-average cost flow $

(f) Perpetual system, moving-average cost flow $

Question 1

A worksheet is composed of multiple workbooks.

True

False

Question 2

A1 contains 3 and A2 contains 4. Cell B2 contains = $A$1 ^ $A$1.

What value will cell C2 display if you copy the formula from cell B2 to cell C2?

0

27

12

16

Question 3

Which of the following cannot be a cell reference?

cell1

B3

$C5

$F$3

none of the above is correct

Question 4

What are the 3 most common types of data that are used in a worksheet cell?

Group of answer choices

text, numbers, and formulas

text, numbers, and values

text, sheets, and formulas

names, values, and formulas

none of the above is correct

Question 5

If cell A1 has a 2 in it, cell B5 has a 1 in it, cell C2 has a 5 in it, and cell D1 has =C2 - B5 + A1 in it, what is displayed in cell D1?

3

4

6

7

this formula has a syntax error in it

Question 6

If cell A1 has a 2 in it, cell B5 has a 1 in it, cell C2 has a 5 in it, and cell D1 has =2 * C2 -( B5 + A1) in it, what is displayed in cell D1?

2

4

7

11

none of the above is correct

Question 7

If cell A1 has a 2 in it, cell B5 has a 1 in it, cell C2 has a 5 in it, and cell D1 has = 2 * (C2 - B5) + A1 in it, what is displayed in cell D1?

4

5

10

11

none of the above is correct

Question 8

If cell A1 has a 2 in it, cell B5 has a 1 in it, cell C2 has a 5 in it, and cell D1 has = 2 * C2 - B5 + A1 in it, what is displayed in cell D1?

5

6

11

none of the above is correct

Question 9

In the formula below, which operator will a worksheet evaluate first?

=A2+B2*(2-5/C3)

=

+

*

-

/

Flag this Question

Question 10

In the formula below, which operation will a worksheet perform first?

=A2+B2*2-5/C3

=

+

*

-

/

Question 11

If cell A1 has 3 in it, cell B2 has 2 in it, what is the value displayed in cell B3 if it contains the following formula?

= 2*A1^B2+1

216

37

19

3

none of the above

Question 12

Which of the choices below is the correct way to express the mathematical value π in a worksheet?

p

pi

=pi

=PI

=PI()

Question 13

If A1 has 3 in it and A2 has 5 in it, what is the value in cell B3 if it contains the following formula?

=SQRT( A1 + 3 * A2 - 2 )

1.73...

2.236...

2.828...

3.46...

4

Question 14

Which formula below is a correct implementation of the square root of the sum of the squares of B2 and C3?

Group of answer choices

=SQRT( B2 + C3 )

=SQRT( B2 ^ 2 + C3 ^ 2)

=SQRT( B2 + C3 ) ^ 2

=SQRT( B2 ^ 2 ) + SQRT( C3 ^ 2 )

none of the above

Question 15

Which is the correct formula in a spreadsheet program to calculate x in the equation 10^x = 27?

=LOG10( 27 )

=SIN( 27 )

=LOG( 10, 27 )

=LN ( 20 )

none of the above

Question 16

Which of the following is NOT an acceptable range in a worksheet?

F2:G4

G, H

A1:A3

B3:B1

Question 17 1 pts

The formula below is in cell C5. If the formula is copied and pasted into D6, how will it appear?

= A1^(2-B2)

Group of answer choices

= B2^(2-C3)

= A1*(2-B2)

= C5^(2-D6)

= A1^(2-B2)

none of the above

Question 18

Which formula below has a syntax error in it?

= A2 + A3 - EXP( A4 )

= A2 + A3 - SQRT( A3 - A4 )

= LOG10(A2 + A3 - LOG10( A4 )

= A2 + 3 * A3 - PI()

= LN( SQRT( A2 + A3 - A4) )

Question 19

A spreadsheet has -2 in cell A3 and 4 in cell B7. Exactly what will be displayed in cell C5 if it contains exactly the following (be careful!):

B7/A3

Group of answer choices

0

-2

2

B7/A3

Question 20

In a worksheet, cell A1 contains 5 and A2 contains miles. What is displayed in cell B4 if it contains the formula

=A1 + A2?

5miles

5 miles

A1 + A2

error message

5

1. Consider the number of days absent from a random sample of six students during a semester: A= {2, 3, 2, 4, 2, 5}
   1. Compute the arithmetic mean, geometric mean, median, and mode by hand and verify the results using R
      1. Arithmetic Mean: X=i=1nXin=2+3+2+4+2+56=3

mean(data2$absent)

[1] 3

2. Geometic Mean: GMx=Πi=1nX11n=2∙3∙2∙4∙2∙516=2.79816

>gmean <- prod(data2$absent)^(1/length(data2$absent))

> gmean

[1] 2.798166

3. Median: X=12n+1th, Xi2,2,2,3,4,5, n=6=126+1th ranked value=3.5, value=2.5 days absent

>median(data2$absent)

[1] 2.5

4. Mode: Most frequent value=2

> mode <- names(table(data2$absent)) [table(data2$absent)==max(table(data2$absent))]

> mode

[1] "2"

2. Compute the variance, standard deviation, and coefficient of variation by hand and verify the results using R.
   1. Sample Variance: S2=i=1nXi-X2n-1=2-32+3-32+2-324-322-325-326-1=85=1.6

> var(data2$absent)

[1] 1.6

2. Sample Standard Deviation: s=s2=i=1nXi-X2n-1=1.6=1.26491

> sd(data2$absent)

[1] 1.264911

3. Coefficient of Variation: CV=SX=1.264912.5=.421637

> cv <- abs(sd(data2$absent)/mean(data2$absent))

> cv

[1] 0.421637

3. Compute the interquartile range of this data by hand and with R

> IQR(data2$absent, type=6)

[1] 2.25

4. Display the data above with a well‐formatted and well‐labeled pie chart created with R.  Recall that with a pie chart, the slices sum to 100 percent, so the slice labeled “2 days absent” should be 50 percent of the pie.

Pie Chart with Percentages

slices <- c(50, 16.6666667, 16.6666667, 16.6666667)

lbls <- c("2 days absent", "3 days absent", "4 days absent", "5 days absent")

pct <- round(slices/sum(slices)*100)

lbls <- paste(lbls, pct) # add percents to labels

lbls <- paste(lbls,"%",sep="") # ad % to labels

pie(slices,labels = lbls, col=rainbow(length(lbls)),

    main="Pie Chart of Absences")

5. Display the data above with a well‐labeled and well‐formatted frequency distribution (histogram) using R.

x <- data2$absent

> h<-hist(x, breaks=10, col="magenta", xlab="# of student absences",

+         main="Histogram of student absences")

> xfit<-seq(min(x),max(x),length=40)

> yfit<-dnorm(xfit,mean=mean(x),sd=sd(x))

> yfit <- yfit*diff(h$mids[1:2])*length(x)

> lines(xfit, yfit, col="blue", lwd=2)

6. Use the relationship between the mean and median to determine whether the distribution above is symmetrical, negatively skewed or positively skewed.  Explain.
   1. Mean > Median = 3 > 2.5, the distribution above is positively skewed.
7. Calculate excess kurtosis using the formula from lecture.  Is this distribution leptokurtic, mesokurtic, or platykurtic?  Explain.  Compared to the normal distribution with the same variance, does this distribution exhibit fatter tails?  Briefly explain
   1. 1ni=1nxi-X41ni=1nxi-X22=162-34+3-34+2-34+4-34+2-34+5-34162-32+3-32+2-32+4-32+2-32+5-322=103169=158≈1.875
   2. Excess kurtosis = kurtosis – 3 = 1.875 – 3 = -1.125, -1.125 < 3
   3. This distribution is platykurtic as excess kurtosis < 0, kurtosis < 3
   4. No it will exhibit thinner tails than a normal distribution.

Suppose someone claims that the population mean is 5 days absent (?: ? =5). What is the alternative hypothesis?  Can you reject the null hypothesis at the 5‐percent and 1‐percent levels of significance?  Use the critical value, p‐value, and confidence interval approaches both “by hand” and with R.  In the “by hand” approach, you can use R (or a statistical table) to get the critical values. ????

A researcher would like to evaluate the effectiveness of a pain-relief patch designed for lower back pain. Prior to testing the patch, each of n = 4 patients rates the current level of back pain on a scale from 1 to 8. After wearing the patch for 90 minutes, a second pain rating is recorded. The data are as follows.

​

                                                Before        After

                                          __________________

                   G = 36                  6          2

                  G² = 784                6          2

                ΣX² = 192                4          4

                                                8          4

                                         ______________________

                                            T = 24   T = 12

                                          SS = 8    SS = 4

Perform a Repeated Measures ANOVA and then analyze the data with a repeated measures t-test. Use the .05 level of significance for both.