Another student must pass through 12 sets of traffic lights on his way to university each day. Suppose

that each of the lights is green 36% of the time, yellow 5% of the time, and red 59% of the time.

Suppose it is known that the traffic lights function independently.

(a) What is the probability that the student encounters exactly five red lights on his way to university

one day?

(b) What is the probability that the student encounters at least three green lights on his way to

university one day?

(c) In a five-day school week, what is the probability that the student encounters exactly seven yellow

lights on his way to university?

A study of hospital admissions in New York State found that of the admissions led to treatment-caused injuries. One-seventh of these treatment-caused injuries resulted in death, and one-fourth were caused by negligence. Malpractice claims were filed in one out of cases involving negligence, and payments were made in one out of every two claims.

a. What is the probability a person admitted to the hospital will suffer a treatment-caused injury due to negligence (to 2 decimals)?

b. What is the probability a person admitted to the hospital will die from a treatment caused injury (to 3 decimals)?

c. In the case of a negligent treatment-caused injury, what is the probability a malpractice claim will be paid(to 5 decimals)?

An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.

a. What is the probability of finding oil (to 1 decimal)?

b. After feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test are given below.

Given the soil found in the test, use Bayes' theorem to compute the following revised probabilities (to 4 decimals).

What is the new probability of finding oil (to 4 decimals)?

According to the revised probabilities, what is the quality of oil that is most likely to be found?

- Select your answer -High qualityMedium qualityNo oil

A sample of 45 entrepreneurs worked an average of 52 hours a week. The population is approximately normally distributed with a standard deviation of 20 hours per week. You want to test whether there is sufficient evidence at the α = 0.10 significance level that entrepreneurs work more than 48 hours per week.

(a) Define the parameter to be tested.

(b) What is the null hypothesis (H0)? What is the alternative hypothesis (H1)?

(c) Specify the test statistic and identify its (approximate) distribution if H0 is true.

(d) Compute the observed value of the test statistic.

(e) Compute the p-value.

(f) Report the strength of the evidence against H0 in favour of H1.

(g) Report the estimated value of the parameter along with the estimated standard error.

(h) If we are asked to test H0 at the significance level α, compare α with the p-value and reject H0 exactly when the p-value ≤ α. Explain your decision in terms of the number of hours worked per week by entrepreneurs.

How do you interpret the unstandardized regression coefficient for a predictor variable? If the regression coefficient for a predictor variable is .52, what does that mean? If the regression coefficient for a predictor variable is -.47, what does that mean?

In the last few years, many research studies have shown that the purported benefits of hormone replacement therapy (HRT) do not exist, and in fact, that hormone replacement therapy actually increases the risk of several serious diseases. A four-year experiment involving 4432 women was conducted at 33 medical centres. Half of the women took placebos and half took a prescription drug, a widely prescribed type of hormone replacement therapy. There were

x₁ = 48

cases of dementia in the hormone group and

x₂ = 20

in the placebo group. Is there sufficient evidence to indicate that the risk of dementia is higher for patients using the prescription drug? Test at the 1% level of significance. (Round your answers to two decimal places.)

1-2. Null and alternative hypotheses:

H₀: (p₁ − p₂) = 0 versus H_a: (p₁ − p₂) < 0H₀: (p₁ − p₂) = 0 versus H_a: (p₁ − p₂) ≠ 0     H₀: (p₁ − p₂) ≠ 0 versus H_a: (p₁ − p₂) = 0H₀: (p₁ − p₂) < 0 versus H_a: (p₁ − p₂) > 0H₀: (p₁ − p₂) = 0 versus H_a: (p₁ − p₂) > 0

3. Test statistic:  z =  

4. Rejection region:  If the test is one-tailed, enter NONE for the unused region.

z >

z <
5. Conclusion:

H₀ is not rejected. There is sufficient evidence to indicate that the risk of dementia is higher for patients using the prescription drug.H₀ is rejected. There is sufficient evidence to indicate that the risk of dementia is higher for patients using the prescription drug.     H₀ is not rejected. There is insufficient evidence to indicate that the risk of dementia is higher for patients using the prescription drug.H₀ is rejected. There is insufficient evidence to indicate that the risk of dementia is higher for patients using the prescription drug.

1. Chi-square Test of Independence

A political psychologist is interested in whether the community a person lives in is related to that person's opinion on an upcoming water conservation ballot initiative. The psychologist surveys a random sample of 96 people by phone from three different communities, with the results shown in the table below. At a 10% significance level, is there evidence that opinion on the water conservation ballot initiative depends on community membership?

a. Type in the hypotheses. Please make sure to incorporate the problem context (i.e., do not write X and Y).

b. Type in the test statistic found from the SPSS. This is the value listed in the “Pearson Chi- Square” row under the “Value” column.

c. Type in the p-value found from the SPSS output. This is the value listed in the “Pearson Chi- Square” row under the “Asymptotic Significance (2-sided)” column.

d. Type your decision regarding the null hypothesis.
e. Type in your conclusion using the context and units from the problem.

Ten randomly selected people took an IQ test A, and next day they took a very similar IQ test B. Their scores are shown in the table below.

1. Consider (Test A - Test B). Use a 0.01 significance level to test the claim that people do better on the second test than they do on the first. (Note: You may wish to use software.)

(a) What test method should be used?

A. Matched Pairs
B. Two Sample z
C. Two Sample t

(b) The test statistic is

(c) The critical value is

(d) Is there sufficient evidence to support the claim that people do better on the second test?

A. No
B. Yes


2. Construct a 99% confidence interval for the mean of the differences. Again, use (Test A - Test B).
_____<μ<____

Explain the influence of a level of significance and sample size has on hypothesis testing. Provide an example of the influence and how it impacts business decisions.

(Please show work/step-by-step. Must be legible.)

1. The researcher from the Annenberg School of Communications is interested in studying the factors that influence how much time people spend talking on their smartphones. She believes that gender might be one factor that influences phone conversation time. She specifically hypothesizes that women and men spend different amounts of time talking on their phones. The researcher conducts a new study and obtains data from a random sample of adults from two groups identified as women and men. She finds that the average daily phone talking time among 15 women in her sample is 42 minutes (with a standard deviation of 6). The average daily minutes spent talking on the phone among 17 men in her sample is 38 (with a standard deviation of 5). She selects a 95% confidence level as appropriate to test the null hypothesis.

a) How many degrees of freedom are there?

b) What is the obtained value of the test statistic (t)?

c) What is the critical value of the test statistic (t)? [t-obtained]

d) What decision should the researcher make about the null hypothesis? Be sure to explain your answer (e.g., what numbers provide the basis for this decision?).

1. Construct a Pie Chart:

You obtained the following data related to demographics in your statistics class:

Race                                                      Number of Students

Hispanic                                               15

Asian                                                     10

African American                             12

Caucasian                                            19

Native American                               5

What can you infer from your data?

2. Construct a Bar Graph:

You obtained the following data related to demographics in your statistics class:

Religion                                                               Number of Students

Christian                                                              17

Muslim                                                                 18

Buddhist                                                              19

Catholics                                                              20

Not Religious                                                      24

What can you infer from your data?

3. Construct a Line Graph:

A professor constructed a new personality test and wants to test its construct validity. She administers the test to her students and assesses the construct validity.

Person                                                                  Construct validity

1                                                                              34

2                                                                              25

3                                                                              15

4                                                                              16

5                                                                              19

6                                                                              25

7                                                                              22

8                                                                              30

9                                                                              14

10                                                                           10

11                                                                           8

12                                                                           20

What can you infer from your data?

4. Construct a Histogram:

In a study of modeling, one group of 20 children saw an adult acting aggressively on videotape. Later each child was placed in a room where he or she was given the opportunity to behave aggressively toward a Bobo doll (a humanlike dummy). The researchers recorded the number of aggressive acts towards the Bobo doll by each child in a 15-minute period. Here are the results:

Number of Aggressive Acts:

25

23

23

23

22

22

21

21

21

21

21

19

19

19

19

18

18

17

17

10

What can you infer from the data?

A technology student project group worked with a machine shop that employs a CNC lathe in the machining of a part produced for a heavy equipment manufacturer. Some summary statistics for a diameter on the part obtained from 25 samples of n=4 parts turned on the lathe are given below. The units are inches.

Sample                                   x-bar                                       R

                 1                                      1.18093                                  .0001

                 2                                      1.18085                                  .0002

                 3                                      1.18095                                  .0002

                 4                                      1.18063                                  .0008

                 5                                      1.18053                                  .0007

                 6                                      1.18053                                  .0005

                 7                                      1.18053                                  .0005

                 8                                      1.18195                                  .0001

                 9                                      1.18100                                  .0003

                10                                     1.18095                                  .0001

   55                            Sum 11.80885                                 .0007

Find retrospective control limits for the values above (both means and ranges). What do the x-bar and R values indicate about the stability of the turning process?

A technology student project group worked with a machine shop that employs a CNC lathe in the machining of a part produced for a heavy equipment manufacturer. Some summary statistics for a diameter on the part obtained from 25 samples of n=4 parts turned on the lathe are given below. The units are inches.

Sample                                   x-bar                                       R

                 1                                      1.18093                                  .0001

                 2                                      1.18085                                  .0002

                 3                                      1.18095                                  .0002

                 4                                      1.18063                                  .0008

                 5                                      1.18053                                  .0007

                 6                                      1.18053                                  .0005

                 7                                      1.18053                                  .0005

                 8                                      1.18195                                  .0001

                 9                                      1.18100                                  .0003

                10                                     1.18095                                  .0001

55 Sum 11.80885 .0007

Find retrospective control limits for the values above (both means and ranges). What do the x-bar and R values indicate about the stability of the turning process

Dean takes his boat out fishing every weekend. His current boat is still in okay condition, but he decides he’d like to buy a new one. He finds the boat of his dreams for $20,950. He does some research and finds that his credit union will give him a 5-year loan with an APR of 4.25% if he makes a down payment of 18%.

1. What is the amount of Dean’s down-payment?   

2. What is the loan amount that Dean will be financing?

3. What will his monthly payments be on the loan?

4. What is the total amount Dean will pay for his boat if he finances the purchase?

5. How much interest will Dean pay the credit union over the life of the loan?   

Sam, Dean’s younger brother, tries to convince Dean to save up for a new boat instead of getting a loan. He tells Dean that the credit union has a savings account option that offers an APR of 1.2% compounded monthly, so long as the account maintains a minimum balance of $2000.

6. Since Dean has the down payment amount already, if he uses that to start a savings account with the credit union, then adds $200 to the account each month, how much will he have at the end of 5 years?

7. If Dean starts the savings account with his down payment money, how much would he have to deposit each month for 5 years to end up with the $20,950 he needs for the boat of his dreams?

8. If Dean follows the savings plan from problem 7, how much total will he have deposited into the savings account at the end of the 5 years?

9. If Dean follows the savings plan from problem 7, how much interest will he have earned in the savings account over the course of the 5 years?

10. Compare the total Dean would pay on the loan to the total Dean would deposit into the savings account. How much would Dean save by going with the savings option?

11. If Dean decides he wants to save up for the boat as fast as possible, how long would it take the account to reach the full value of $20,950 if he uses the down payment money to start the account then adds $400 each month? Give the answer as years with 2 decimal places!

@ Write several paragraphs discussing the advantages and disadvantages of both methods for Dean. Explain the reasons a person might choose to finance a purchase and the reasons that a person might choose to save up for a purchase. If you were in Dean’s position, what would you do and why? Be sure to use your work and answers from the proceeding questions to support your explanations and assertions.

I really need the last part. Please, write at least three paragraphs and your own words in detail question.

THANKS.

We are creating a new card game with a new deck. Unlike the normal deck that has 13 ranks (Ace through King) and 4 Suits (hearts, diamonds, spades, and clubs), our deck will be made up of the following.

Each card will have:
i) One rank from 1 to 15.
ii) One of 5 different suits.

Hence, there are 75 cards in the deck with 15 ranks for each of the 5 different suits, and none of the cards will be face cards! So, a card rank 11 would just have an 11 on it. Hence, there is no discussion of "royal" anything since there won't be any cards that are "royalty" like King or Queen, and no face cards!

The game is played by dealing each player 5 cards from the deck. Our goal is to determine which hands would beat other hands using probability. Obviously the hands that are harder to get (i.e. are more rare) should beat hands that are easier to get.

g) How many different ways are there to get a full house (i.e. 3 of a kind and a pair, but not all 5 cards the same rank)?

What is the probability of being dealt a full house?
Round your answer to 7 decimal places.

h) How many different ways are there to get a straight flush (cards go in consecutive order like 4, 5, 6, 7, 8 and all have the same suit. Also, we are assuming there is no wrapping, so you cannot have the ranks be 13, 14, 15, 1, 2)?

What is the probability of being dealt a straight flush?
Round your answer to 7 decimal places.