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 pvalue.
2) At a 0.05 level of significance, what is your conclusion?
A)Reject H_{0}. We conclude that the employment plan is independent of the type of company.
b)Do not reject H_{0}. We cannot conclude that the employment plan and the type of company are not independent.
c) Reject H_{0}. We conclude that the employment plan is not independent of the type of company.
d)Do not reject H_{0}. 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.
In: Statistics and Probability
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.
In: Statistics and Probability
Your professor wants to know if all tests are created equal.
What is the FStat? 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 
In: Statistics and Probability
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?
In: Statistics and Probability
(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
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  
In: Statistics and Probability
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)
In: Statistics and Probability
18. Explain in your own words the reasons, process and limitations of the OLS estimator.
In: Statistics and Probability
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.
In: Statistics and Probability
Data for the two variables X & Y is given below:
(4,3); (6,5); (8,6); (11, 10); (13, 11); (15,13)
In: Statistics and Probability
The file CD Rate contains yields for a oneyear certificate of deposit (CD) and a fiveyear 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  OneYear  FiveYear 
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 
ELoan  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 
In: Statistics and Probability
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 pvalue.
b) Discuss any dependence that exists between the type of ticket and type of flight.
In: Statistics and Probability
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 ChiSquare calculated by showing each step of the calculations. (20 points) If you don’t show each step, you will get 0
c) Find the ChiSquare 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 
In: Statistics and Probability
n one school district, there are 89 elementary school (K5)
teachers, of which 18 are male (or maleidentifying). 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≤
In: Statistics and Probability
You are working for an investment firm that focuses their efforts on investing with a goal of providing income for aged peoples throughout their final years. Every financial product that you sell has a minimum acceptable interest rate of return, but obviously no maximum acceptable value, as the goal is to maximize the return for your customers as much as possible.
To determine if the process by which you are selecting the financial products is doing a capable job or not, which value would you examine since "larger is better" is your firm's motto when it comes to the rates of return you secure for your clients?
Сpl
Cp
Cpu
Cpk
In: Statistics and Probability
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.
In: Statistics and Probability