The British Department of Transportation studied to see if people avoid driving on Friday the 13th.   They did a traffic count on a Friday and then again on a Friday the 13th at the same two locations ("Friday the 13th," 2013). The data for each location on the two different dates is in table #9.2.6. Estimate the mean difference in traffic count between the 6th and the 13th using a 90% level.
Table #9.2.6: Traffic Count
Dates 6th 13th
1990, July 139246 138548
1990, July 134012 132908
1991, September 137055 136018
1991, September 133732 131843
1991, December 123552 121641
1991, December 121139 118723
1992, March 128293 125532
1992, March 124631 120249
1992, November 124609 122770
1992, November 117584 117263

A marketing research firm wishes to compare the prices charged by two supermarket chains—Miller’s and Albert’s. The research firm, using a standardized one-week shopping plan (grocery list), makes identical purchases at 10 of each chain’s stores. The stores for each chain are randomly selected, and all purchases are made during a single week. It is found that the mean and the standard deviation of the shopping expenses at the 10 Miller’s stores are x1¯¯¯¯?=?$114.14x1¯?=?$114.14 and s₁= 1.12. It is also found that the mean and the standard deviation of the shopping expenses at the 10 Albert’s stores are x2¯¯¯¯?=?$113.14x2¯?=?$113.14 and s₂= 1.67.

(a) Calculate the value of the test statistic. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Test statistic          

(b) Calculate the critical value. (Round your answer to 2 decimal places.)

Critical value          

(c) At the 0.02 significance level, what it the conclusion?

Suppose two independent random samples of sizes n₁ = 9 and n₂ = 7 that have been taken from two normally distributed populations having variances σ12σ21 and σ22σ22 give sample variances of s₁² = 117 and s₂² = 19.

(a) Test H₀: σ12σ21 = σ22σ22 versus H_a: σ12σ21 ≠≠ σ22σ22 with σσ = .05. What do you conclude? (Round your answers to 2 decimal places.)

(b) Test H₀: σ12σ21< σ22σ22versus H_a: σ12σ21 > σ22σ22 with σσ = .05. What do you conclude? (Round your answers to 2 decimal places.)

The correlation coefficient r is a sample statistic. What does it tell us about the value of the population correlation coefficient ρ (Greek letter rho)? You do not know how to build the formal structure of hypothesis tests of ρ yet. However, there is a quick way to determine if the sample evidence based on ρ is strong enough to conclude that there is some population correlation between the variables. In other words, we can use the value of r to determine if ρ ≠ 0. We do this by comparing the value |r| to an entry in the correlation table. The value of α in the table gives us the probability of concluding that ρ ≠ 0 when, in fact, ρ = 0 and there is no population correlation. We have two choices for α: α = 0.05 or α = 0.01. (a) Look at the data below regarding the variables x = age of a Shetland pony and y = weight of that pony. Is the value of |r| large enough to conclude that weight and age of Shetland ponies are correlated? Use α = 0.05. (Use 3 decimal places.) x 3 6 12 21 24 y 60 95 140 190 172 r Incorrect: Your answer is incorrect. critical r Incorrect: Your answer is incorrect. Conclusion Reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated. Reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated. Fail to reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated. Fail to reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated. Correct: Your answer is correct. (b) Look at the data below regarding the variables x = lowest barometric pressure as a cyclone approaches and y = maximum wind speed of the cyclone. Is the value of |r| large enough to conclude that lowest barometric pressure and wind speed of a cyclone are correlated? Use α = 0.01. (Use 3 decimal places.) x 1004 975 992 935 970 924 y 40 100 65 145 65 146 r critical r Incorrect: Your answer is incorrect. Conclusion Reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. Reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. Fail to reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. Fail to reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.

1.

Suppose that

Superman is the favorite hero of

3

5%

of

all DC Comics fans, Batman is the

favorite of 26% of fans, Wonder Woman is the favorite of 19%, Green Lantern is the favorite

of 12%, and the

Flash is the favorite of all the rest of fans

.

a)

If a

DC Comics fan

is selected at random, what is the

probability that

:

i.

T

he Flash is that person’s favorite superhero

?

ii.

T

he person’s favorite superhero is Batman or Wonder Woman?

iii.

T

he person’s

favorite superhero is not Superman

?

b)

If you were to randomly select

five

DC Comics fans

, what is the probability that:

i.

Batman

is the favorite superhero of all five people

?

2

ii.

No

ne of the

five

people

identify Green Lantern as their favorite superhero

?

iii.

All five people identify

Green Lantern

as their favorite superhero

or

all five identify

Wonder Woman

as their favorite

?

iv.

N

ot

all

five

people identify

the Flash

as their favorite superhero

?

v.

Superman is the favorite superhero of

at least

one of the

five

people

?

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

It is known that 82% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces 60 new products, find the following probabilities. (Round your answers to four decimal places.)

(a) within 2 years 47 or more fail


(b) within 2 years 58 or fewer fail


(c) within 2 years 15 or more succeed


(d) within 2 years fewer than 10 succeed

A palindrome is a string whose reversal is identical to the string. For example, 110010011 is a palindrome. So are BOB and KAYAK. How many bit strings of length ?? are palindromes? Explain your solution clearly.

When you develop a research project, you need to have a reliable and valid method of measurement in your study. Using your anticipated research proposal, how will you address the issues of reliability and validity? What concerns do you have over reliability and validity in your study and how will you overcome these concerns? Next, read two of your classmates’ posts and analyze how they addressed reliability and validity in their studies. Do you have any recommendations for improving reliability and validity?

A regional automobile dealership sent out fliers to prospective customers indicating that they had already won one of three different​ prizes: an automobile valued at ​$20000​, a ​$150 gas​ card, or a ​$5 shopping card. To claim his or her​ prize, a prospective customer needed to present the flier at the​ dealership's showroom. The fine print on the back of the flier listed the probabilities of winning. The chance of winning the car was 1 out of 31,433​, the chance of winning the gas card was 1 out of 31,433 and the chance of winning the shopping card was 31,431 out of 31,433. Complete parts​ (a) through​ (d).

a. How many fliers do you think the automobile dealership sent​ out?

b. Using your answer to (a) and the probabilities listed on the flier, what is the expected value of the prize won by a prospective customer receiving a flier?

c.Using your answer to (a) and the probabilities listed on the flier, what is the standard deviation of the value of the prize won by a prospective customer receiving a flier?

d.Do you think this is an effective promotion? why or why not?

1. Using the 'pulp' data from the faraway package in R, determine whether there are any differences between the operators. What is the nature of these differences? (Note; You must do multiple comparisons). Please use R or R studio code. Thanks!

Case Problem - Regression

Are you going to hate your new job?

Getting a new job can be exciting and uplifting. But what if you discover that after a short time on the job, that you hate your new job? Is there any way to determine ahead of time whether you will love or hate your new job? According to the Wall Street Journal, there are a few things to look for in the interview that might help you to determine whether you will be happy on that job.

A study conducted by the University of Connecticut posed several questions to employees to ascertain their job satisfaction. Themes included: relationship with the supervisor, overall quality of the work environment, total weekly hours worked, and opportunity for advancement at the job. Nineteen employees were asked to rate their job satisfaction on a scale of 0-100, with 100 being perfectly satisfied. The results of the survey are as follows. Assume that the relationship with a supervisor is rated from 0-50, with 50 as excellent. Overall workplace quality rated from 0-100, with 100 representing an excellent environment and opportunities for advancement on a scale of 0-50 with 50 representing excellent opportunity.

Job                   Relationship                 Overall Quality              Total Hrs.                      Opportunities

Satisfaction       w/ Supervisor               Work Environ                Worked/wk                  Advancement

55                    27                                65                                50                                42

20                    12                                13                                60                                28

85                    40                                79                                45                                7

65                    35                                53                                65                                48

45                    29                                43                                40                                32

70                    42                                62                                50                                41

35                    22                                18                                75                                18

60                    34                                75                                40                                32

95                    50                                84                                45                                48

65                    33                                68                                60                                11

85                    40                                72                                55                                33

10                    5                                  10                                50                                21

75                    37                                64                                45                                42

80                    42                                82                                40                                46

50                    31                                46                                60                                48

90                    47                                95                                55                                30

75                    36                                82                                70                                39

45                    20                                42                                40                                22

65                    32                                73                                55                                12

1. Develop a multiple regression model and analyze the data above related to job satisfaction. Use the four step analytical process to analyze the data. Test at the 0.05 level of significance and discuss in detail.

2. Of the variables above that are related to job satisfaction, which variables are stronger predictors of job satisfaction? Are other variables not mentioned here, potentially related to job satisfaction? Discuss in detail.

A factorial experiment was designed to test for any significant differences in the time needed to perform English to foreign language translations with two computerized language translators. Because the type of language translated was also considered a significant factor, translations were made with both systems for three different languages: Spanish, French, and German. Use the following data for translation time in hours.

Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use a= .05.

Complete the following ANOVA table (to 2 decimals, if necessary). Round your p-value to 4 decimal places.

A Saskatchewan farm machinery manufacturing company has developed a prototype of two machinery models (A and B). The manufacturer wishes to select one of these machines for further manufacturing. Also the manufacturer is under no obligation to select any of these 2 machines. The company has hired you to make a recommendation to the manufacturer not eh selection of the best alternative. In further discussion with the manufacturer you select the following attributes of the decision problem: a) manufacturers major motivation in selecting the best farm machinery in economic-improve the level of earnings for the company b)major uncertainty facing the selection process is future markets. Given above attributes, you decide to undertake a market survey, which resulted in 3 possible types of markets: Bouyant, steady state and Depressed. You also estimated the there are 3 types of markets prevail 50:20:30 percent, respectively, of the time in the future. You also estimated the net revenues of the company from sales of 2 types of machinery in thousands of dollars shown below:

Using a decision three model, provide your recommendation to the farm machinery manufacturing company.

The director of admissions at the University at the University of Maryland, University College is concerned about the high cost of textbooks for the students each semester. A sample of 25 students enrolled in the university indicates that x(bar) = $315.40 and s = $43.20.

A mean that is not in a confidence interval is rejected by the confidence interval, and we say the evidence against the mean is significant. At the 0.10 level of significance, is there evidence against mean $300?

1. No, because 300 is below the lower limit of the confidence interval
2. Yes, because 300 is below the lower limit of the confidence interval
3. No because 300 is in the confidence interval
4. Yes, because 300 is in the confidence interval

A magazine reported that at the top 50 business schools in a​ region, students studied an average of 17.8 hours. Set up a hypothesis test to try to prove that the mean number of hours studied at your school is different from the reported 17.8 hour benchmark. Complete parts​ (a) through​ (c) below.

a. State the null and alternative hypotheses. Choose the correct answer below.

A. Upper H 0​: alpha not equals 17.8 Upper H 1​: alpha equals 17.8

B. Upper H 0​: beta not equals 17.8 Upper H 1​: beta equals 17.8

C. Upper H 0​: muequals17.8 Upper H 1​: Upper X overbarnot equals17.8

D. Upper H 0​: Upper X overbarequals17.8 Upper H 1​: Upper X overbarnot equals17.8

E. Upper H 0​: alpha equals 17.8 Upper H 1​: beta not equals 17.8

F. Upper H 0​: munot equals 17.8 Upper H 1​: Upper X overbar equals17.8

G. Upper H 0​: alphaequals17.8 Upper H 1​: alphanot equals17.8

H. Upper H 0​: muequals17.8 Upper H 1​: munot equals17.8

I. Upper H 0​: Upper X overbarnot equals17.8 Upper H 1​: Upper X overbarequals17.8

J. Upper H 0​: alphanot equals17.8 Upper H 1​: betaequals17.8

K. Upper H 0​: munot equals17.8 Upper H 1​: muequals17.8

L. Upper H 0​: betaequals17.8 Upper H 1​: betanot equals17.8

b. What is a Type I error for your​ test?

A. Concluding that the mean number of hours studied at your school is different from the reported 17.8 hour benchmark when in fact it is different

B. Concluding that the mean number of hours studied at your school is not different from the reported 17.8 hour benchmark when in fact it is different

C. Concluding that the mean number of hours studied at your school is different from the reported 17.8 hour benchmark when in fact it is not different

c. What is a Type II error for your​ test?

A. Concluding that the mean number of hours studied at your school is not different from the reported 17.8 hour benchmark when in fact it is different

B. Concluding that the mean number of hours studied at your school is different from the reported 17.8 hour benchmark when in fact it is different

C. Concluding that the mean number of hours studied at your school is different from the reported 17.8 hour benchmark when in fact it is not different

Describe the key difference between the separation of between treatment variability for the one-factor independent measures ANOVA and the two-factor independent measures factorial ANOVA.