A Deloitte employment survey asked a sample of human resource executives how their company planned to change its workforce over the next 12 months. A categorical response variable showed three options: the company plans to hire and add to the number of employees, the company plans no change in the number of employees, or the company plans to lay off and reduce the number of employees. Another categorical variable indicated if the company was private or public. Sample data for 180 companies are summarized as follows.

Employment Plan	Company
	Private	Public
Add Employees	37	32
No Change	19	34
Lay Off Employees	16	42

1) Conduct a test of independence to determine if the employment plan for the next 12 months is independent of the type of company.

-State the null and alternative hypotheses.

-Find the value of the test statistic.

-Find the p-value.

2) At a 0.05 level of significance, what is your conclusion?

A)Reject H₀. We conclude that the employment plan is independent of the type of company.

b)Do not reject H₀. We cannot conclude that the employment plan and the type of company are not independent.   

c) Reject H₀. We conclude that the employment plan is not independent of the type of company.

d)Do not reject H₀. We cannot conclude that the employment plan and the type of company are independent.

3)Discuss any differences in the employment plans for private and public companies over the next 12 months. (Round your numeric answers to two decimal places.

A)Employment opportunities look to be about the same for both public and private companies, with high proportions of "no change" and "lay off employees" planned for both.

b)Employment opportunities look to be about the same for both public and private companies, with high proportions of "add employees" planned for both.    

c)Employment opportunities look to be much better for private companies, while public companies have the greater proportions of "no change" and "lay off employees" planned.

d)Employment opportunities look to be much better for public companies, while private companies have the greater proportions of "no change" and "lay off employees" planned.

Three people are brought into a room. A hat is placed on each person’s head. The hat is equally likely to be Red or Blue. (So each of the 8 possibilities is equally likely.) Each person sees the colors of the other people’s hats, but not their own. Each person, without communication, writes down one of the following: "My hat is red", "My hat is blue" or "Pass". All three people will be put in jail unless (a) at least one of them doesn’t pass, and (b) everyone who doesn’t pass is right about his/her own hat color. Importantly, they can agree ahead of time on a strategy, with the hopes of not going to prison.

(a) What is the probability that they are not sent to prison if each person guesses the color of his/her own hat?

(b) What is the probability that they are not sent to prison if two of them pass and 1 of them guesses?

(c) What is the probability that they are not sent to prison if they use the following strategy: Each person looks at the other two hats. If they are both blue, then the person guesses red. If they are both red, then the person guesses blue. If they are different, the person passes.

Your professor wants to know if all tests are created equal.

What is the F-Stat? Use Excel.

EXAM1	EXAM2	EXAM3	FINAL
73	80	75	65.86667
93	88	93	80.16667
89	91	90	78
96	98	100	84.93333
73	66	70	61.53333
53	46	55	43.76667
69	74	77	64.56667
47	56	60	49.83333
87	79	90	75.83333
79	70	88	71.06667
69	70	73	61.1
70	65	74	61.1
93	95	91	79.73333
79	80	73	65.86667
70	73	78	64.13333
93	89	96	83.2
78	75	68	63.7
81	90	93	79.3
88	92	86	76.7
78	83	77	68.9
82	86	90	76.7
86	82	89	75.83333
78	83	85	75.83333
76	83	71	64.56667
96	93	95	83.2

A supervisor's annual performance rating on a scale of 1 (lowest) to 10 (highest) for each of 20 employees. This is an example of what scale of measurement?

(Covering concepts for Chapter 3 and 8)

The following attached file presents the annual returns for two mutual funds offered by the investment giant Fidelity. The Fidelity Select Automotive Fund invests primarily in companies engaged in the manufacturing, marketing, or sales of automobiles, trucks, specialty vehicles, parts, tires and related services. The Fidelity Gold Fund invests primarily in companies engaged in exploration, mining, processing, or dealing in gold and, to a lesser degree, in other precious metals and minerals.

In a report, use the above information and attached file to

1. Calculate descriptive statistics to compare the returns of the mutual funds using the Data Analysis Descriptive Box.
2. Compare and interpret the mean, median and skewness of Fidelity Select Automotive Fund and Fidelity Select Gold Funds.

3. Compare and interpret the range and the standard deviation of Fidelity Select Automotive Fund and Fidelity Gold Funds.
4. Discuss the range of each funds returns? Is the range the best descriptive measure? Why or Why not?
5. Assess reward by constructing and interpreting 95% confidence intervals for the population mean return. What assumption did you make for interval estimates?

Example p. 314/ Note Use standard deviation as a measure of risk!

Year	Automotive	Gold
2001	22.82	24.99
2002	-6.48	64.28
2003	43.53	32.09
2004	7.11	-9.79
2005	-1.75	40.7
2006	13.33	25.43
2007	0.01	24.93
2008	-61.2	-20.49
2009	122.28	38
2010	46.18	35.25
2011	-26.16	-16.34
2012	26.17	-12.43
2013	46.67	-51.41
2014	2.79	-8.51
2015	0.17	-17.88
2016	-5.83	47.28

Individuals were randomly assigned to three different production processes. The hourly unit of production for the three processes are shown below:

Process1	Process2	Process3
33	33	28
30	35	36
28	30	30
29	38	34

At 5% level of significance, test whether there is the average output of the three processes . Use the critical value approach. Show all the steps and all the computations(10 Marks question)

18. Explain in your own words the reasons, process and limitations of the OLS estimator.

A randomized, double‑blind experiment studied whether magnetic fields applied over a painful area can reduce pain intensity. The subjects were 5050 volunteers with postpolio syndrome who reported muscular or arthritic pain. The pain level when pressing a painful area was graded subjectively on a scale from 00 to 1010 ; (where 00 is no pain, 1010 is maximum pain.)

Patients were randomly assigned to wear either a magnetic device or a placebo device over the painful area for 4545 minutes. A summary is given of the pain scores for this experiment, expressed as means ±± standard deviations.

	Magnetic device (?=29)(n=29)	Placebo device (?=21)(n=21)
Pretreatment	9.6±0.79.6±0.7	9.5±0.89.5±0.8
Post‑treatment	4.4±3.14.4±3.1	8.4±1.88.4±1.8
Change	5.2±3.25.2±3.2	1.1±1.61.1±1.6

(a) Is there good evidence that the magnetic device is better than a placebo equivalent at reducing pain? Let ?1μ1 and ?2μ2 be the mean change in pain for patients given the magnetic device or the placebo device, respectively. State the hypotheses for the appropriate test.

a. ?0:?1−?2=4.1 vs ??:?1−?2≠4.1H0:μ1−μ2=4.1 vs Ha:μ1−μ2≠4.1

b. ?0:?1≤?2 vs ??:?1>?2H0:μ1≤μ2 vs Ha:μ1>μ2

c. ?0:?1−?2=0 vs ??:?1−?2=4.1H0:μ1−μ2=0 vs Ha:μ1−μ2=4.1

d. ?0:?1=?2 vs ??:?1>?2H0:μ1=μ2 vs Ha:μ1>μ2

e. ?0:?1=?2 vs ??:?1≠?2H0:μ1=μ2 vs Ha:μ1≠μ2

f. ?0:?1−?2=4.1 vs ??:?1−?2>4.1H0:μ1−μ2=4.1 vs Ha:μ1−μ2>4.1

g. ?0:?1=?2 vs ??:?1<?2

Give the test statistic and the ?P‑value for the test.

a. ?=1.15,0.10<?<0.20t=1.15,0.10<P<0.20

b. ?=5.95,0.0005<?<0.05t=5.95,0.0005<P<0.05

c. ?=5.95,?<0.0005t=5.95,P<0.0005

d. ?=1.15,0.20<?<0.30t=1.15,0.20<P<0.30

Is there significant difference between the magnetic device and a placebo in relieving pain?

a. There is no evidence that the magnetic device is better than a placebo at relieving pain in this population, on average.

b. There is extremely strong evidence that the magnetic device is better than a placebo at relieving pain in this population, on average.

c. There is significant evidence that the magnetic device is better than a placebo at relieving pain among the study participants.

d. There is some moderate evidence that the magnetic device is better than a placebo at relieving pain in this population, on average.

(b) How much reduction in pain is achieved with the magnetic device? Select the correct 95%95% confidence interval for the mean difference in pain scores before and after treatment among patients given the magnetic device.

a. 3.2 to 5.63.2 to 5.6

b. 3.8 to 6.63.8 to 6.6

c. 4.2 to 6.24.2 to 6.2

d. 4.0 to 6.44.0 to 6.4

What procedure did you use for this confidence interval?

a. The matched pairs ?t procedure

b. The two‑sample ?t procedure

c. The one‑sample ?t procedure

d. None of the options are correct.

Data for the two variables X & Y is given below:

(4,3); (6,5); (8,6); (11, 10); (13, 11); (15,13)

1. Draw scatter plot of X-Y
2. Find correlation coefficient
3. Infer the relation between the two variables

The file CD Rate contains yields for a one-year certificate of deposit (CD) and a five-year CD for 39 banks listed for West Palm Beach, Florida on January 9, 2017. For each type of investment, decide whether the data appear to be approximately normally distributed by:

a. comparing data characteristics to theoretical properties.

b. constructing a normal probability plot

Bank	One-Year	Five-Year
5 Star Bank	1.00	1.60
Alostar Bank of Commerce	1.05	1.66
Amalgamated Bank	0.50	1.10
AmTrust Bank	0.40	1.25
Applied Bank	0.15	0.15
Armed Forces Bank N. A.	0.75	1.75
Auto Club Trust FSB	1.15	1.75
Bank of America	0.05	0.15
Blake & Herbert Bank	0.50	0.65
BlueHarbor Bank	0.50	0.90
BMO Harris Bank NA	0.15	0.75
Busey Bank	0.20	0.75
California First National Bank	1.26	1.80
CBC national Bank	0.45	1.75
Discover Bank	1.15	1.76
EH National Bank	0.95	1.51
E-Loan	1.28	1.80
EverBank	1.35	2.28
First Internet Bank of Indiana	1.21	2.07
First Tennessee Bank NA	0.10	0.55
Goildman Sachs Bank USA	1.20	1.85
Goldwater Bank	1.07	1.25
grantbank	1.06	1.66
Grow Financial FCU	0.45	2.00
Home Savings Bank	1.00	1.90
Live Oak Bank	1.30	1.75
Luana Savings Bank	0.80	1.61
Patriot Bank	0.30	1.01
Pendelton Community Bank	0.35	1.35
PNC Bank	0.10	0.55
Popular Direct	1.28	2.25
Presidential Bank FSB	0.95	1.53
Radius Bank	0.25	1.00
Synchrony	1.25	1.85
TD Bank NA	0.25	0.65
Union Bank	0.25	1.15
Urban Partnership Bank	0.28	0.70
VirtualBank	1.31	1.81
Wells Fargo	0.05	0.35

A magazine subscriber study asked, "In the past 12 months, when traveling for business, what type of airline ticket did you purchase most often?" A second question asked if the type of airline ticket purchased most often was for domestic or international travel. Sample data obtained are shown in the following table.

Type of Ticket	Type of Flight
	Domestic	International
First class	31	24
Business class	93	119
Economy class	518	135

A) Using a 0.05 level of significance, is the type of ticket purchased independent of the type of flight?

-State the null and alternative hypotheses.

-Find the value of the test statistic

-Find the p-value.

b) Discuss any dependence that exists between the type of ticket and type of flight.

2. In one of the firms, the staffs are working in 4 different units. All of them using a statistical package to do their job. The CEO of the firm claims that there is a relationship between the statistical package and units of the firm. The units in the firm are Human Resources, Information Technologies, Accounting, and Finance. The packages used in the firm are EViews, Stata, SPSS Test this claim with 0.05 significance level by using the correct test and showing each calculation step in Ms Word file. You have to use the same steps which we used in the lecture. You can find the steps from lecture slides or recorded video. SEND IT IN MS WORD FORMAT NOT SCREENSHOT

a) Find the expected value for each cell by showing each step of the calculations. (10 points) If you don’t show each step, you will get 0

b) Find the Chi-Square calculated by showing each step of the calculations. (20 points) If you don’t show each step, you will get 0

c) Find the Chi-Square Table value (10 points)

d) Write your decision (10 points)

	EView	Stata	SPSS
HM	40	40	30
IT	50	80	20
Accounting	60	40	10
Finance	50	20	30

n one school district, there are 89 elementary school (K-5) teachers, of which 18 are male (or male-identifying). In a neighboring school district, there are 102 elementary teachers, of which 17 are male. A policy researcher would like to calculate the 99% confidence interval for the difference in proportions of male teachers.

To keep the signs consistent for this problem, we will calculate all differences as p1−p2. That is, start with the percentage from the first school district and then subtract the percentage from the second district. Failing to do so may end up with “correct” answers being marked as wrong.

Point estimate for the percentage males in the first district:
      ˆp1=
Point estimate for the percentage males in the second district:
      ˆp2=
Point estimate for the difference in percentages between the two districts:
      ˆp1−ˆp2=

Estimate of the standard error for this sampling distribution (distribution of differences):
      √ˆp1(1−ˆp1)n1+ˆp2(1−ˆp2)n2=

Critical value for the 99% confidence level:
      zc.v.=

99% margin of error:
      M.E.=

99% confidence interval:

≤p1−p2≤

The following are the weights, in decagrams, of 10 packages of grass seed distributed by a certain company: 46.4, 46.1, 45.8, 47.0, 46.1, 45.9, 45.8, 46.9, 45.2, and 46.0. Find a 95% confidence interval for the standard deviation of the weights of all such packages of grass seed distributed by this company, assuming a normal population.