Suppose that we are at time zero. Passengers arrive at a train station according to a Poisson process with intensity λ. Compute the expected value of the total waiting time of all passengers who have come to the station in order to catch a train that leaves at time t.

The answer is λt^2/2

A sample of 150 individuals (males and females) was surveyed, and the individuals were asked to indicate their yearly incomes. Their incomes were categorized as follows.

Category 1	$20,000	up to	$40,000
Category 2	$40,000	up to	$60,000
Category 3	$60,000	up to	$80,000

Income Category	Male	Female
Category 1	10	30
Category 2	35	15
Category 3	15	45

We want to determine if yearly income is independent of gender.

a. Compute the test statistic.

b. Using the p-value approach, test to determine if yearly income is independent of gender. Use α = .05. Briefly discuss.

Your leader has asked you to evaluate the defects based on insurance claim type (auto vs. injury). You have a total of 600 claims, with 400 auto, 200 injury, 100 with a defect, and 60 auto or has an injury.

    Provide at least three relevant probabilities for the leader that will be important for use in making business decisions.

    Explain why the selected probabilities are important.

UIT is a computer retail store that sells two kinds of microcomputers: desktops and laptops. The company earns $220 profit on each desktop computer it sells and $500 profit on each laptop. The microcomputers UIT sells are from its wholesaler. This wholesaler can only supply UIT up to 350 desktops and 295 laptops next month. The employees at UIT must spend 30 minutes installing software and checking each desktop computer they sell. The employees spend 50 minutes to complete this process for each of the laptop computers. They expect to have 16000 minutes available from the employees next month. Due to consumers’ demands, the number of desktops cannot be less than the number of laptops. The manager is certain that they can sell all the computer they order, but unsure how many of desktops and laptops they should order to maximize UIT's profit.

(a) Formulate a linear programming model for this problem.

(b) Use the graphical approach to solve the model and report your managerial decision.

(c) Report the total profit for this problem.

(d) The unit profit for a desktop now increases to $450. What will be your revised managerial decision?

(e) Report the revised profit for part (d).

Karin arrives at the post office, which opens at 9:00 a.m., at 9:05 a.m. She finds two cashiers at work, both serving one customer each. The customers started being served at 9:00 and 9:01, respectively. The service times are independent and Exp(8)-distributed. Let Tk be the time from 9:05 until service has been completed for k of the two customers, k = 1, 2. Find ETk for k=1 and 2.

The answer is ET1 =4, ET2 =12.

An automobile manufacturer claims that its van has a 38.4 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 240 vans, they found a mean MPG of 38.1. Assume the standard deviation is known to be 2.0. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to 2 decimal places.

Enter the value of the test statistic.

The response time in milliseconds was determined for three different types of circuits in an electronic calculator. The results are recorded in table:

Curcuit Type	Response (R)	R	R	R	R
1	19	22	20	18	25
2	20	21	33	27	40
3	16	15	18	26	17

(a) What is the value of LSD? Use α=0.01.
Round your answer to two decimal places (e.g. 98.76).

(b) Apply Fisher's LSD method with α=0.01 and state which circuit type differs or circuit types differ.

(c) What is the absolute value of difference between means for circuits 1 and 3?
Round your answer to one decimal place (e.g. 98.7).

(d) Estimate the standard error for comparing the means using the graphical method.
Round your answer to three decimal places (e.g. 98.765).

According to literature on brand loyalty, consumers who are loyal to a brand are likely to consistently select the same product. This type of consistency could come from a positive childhood association. To examine brand loyalty among fans of the Chicago Cubs, 365 Cubs fans among patrons of a restaurant located in Wrigleyville were surveyed prior to a game at Wrigley Field, the Cubs' home field. The respondents were classified as "die-hard fans" or "less loyal fans." Of the 134 die-hard fans, 88.1% reported that they had watched or listened to Cubs games when they were children. Among the 231 less loyal fans, 71.0% said that they watched or listened as children. (Let D = p_die-hard − p_{less loyal}.)

(a) Find the numbers of die-hard Cubs fans who watched or listened to games when they were children. Do the same for the less loyal fans. (Round your answers to the nearest whole number.)

die-hard fans

less loyal fans

(b) Use a one sided significance test to compare the die-hard fans with the less loyal fans with respect to their childhood experiences relative to the team. (Use your rounded values from part (a). Use α = 0.01. Round your z-value to two decimal places and your P-value to four decimal places.)

z	=
P-value	=

Conclusion

____Reject the null hypothesis, there is significant evidence that a higher proportion of die hard Cubs fans watched or listened to Cubs games as children.

____Fail to reject the null hypothesis, there is significant evidence that a higher proportion of die hard Cubs fans watched or listened to Cubs games as children.    

____Fail to reject the null hypothesis, there is not significant evidence that a higher proportion of die hard Cubs fans watched or listened to Cubs games as children.

____Reject the null hypothesis, there is not significant evidence that a higher proportion of die hard Cubs fans watched or listened to Cubs games as children.

(c) Express the results with a 95% confidence interval for the difference in proportions. (Round your answers to three decimal places.)

( ______ , ______ )

Thank you
,

A medical researcher wants to compare the pulse rates of smokers and non-smokers. He believes that the pulse rate for smokers and non-smokers is different and wants to test this claim at the 0.02 level of significance. A sample of 46 smokers has a mean pulse rate of 75, and a sample of 47 non-smokers has a mean pulse rate of 73. The population standard deviation of the pulse rates is known to be 7 for smokers and 10 for non-smokers. Let μ1 be the true mean pulse rate for smokers and μ2 be the true mean pulse rate for non-smokers. Step 1 of 4: State the null and alternative hypotheses for the test. Step 2 of 4: Compute the value of the test statistic. Round your answer to two decimal places. Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to two decimal places. Step 4 of 4: Make the decision for the hypothesis test.

A publisher reports that 42% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 250 found that 35% of the readers owned a particular make of car. Find the value of the test statistic. Round your answer to two decimal places.

The National Student Loan Survey asked the student loan borrowers in their sample about attitudes toward debt. Below are some of the questions they asked, with the percent who responded in a particular way. Assume that the sample size is 1260 for all these questions. Compute a 95% confidence interval for each of the questions, and write a short report about what student loan borrowers think about their debt. (Round your answers to three decimal places.)

(a) "To what extent do you feel burdened by your student loan payments?" 56.9% said they felt burdened.

( _____ , ______ )

  ,

(b) "If you could begin again, taking into account your current experience, what would you borrow?" 55.2% said they would borrow less.

(_____ , ______ )

   

(c) "Since leaving school, my education loans have not caused me more financial hardship than I had anticipated at the time I took out the loans." 33.5% disagreed.

( ____ , _____ )

(d) "Making loan payments is unpleasant but I know that the benefits of education loans are worth it." 58.4% agreed.

( ____ , _____ )

(e) "I am satisfied that the education I invested in with my student loan(s) was worth the investment for career opportunities." 58.6% agreed.

( _____ , _____ )

  , (f) "I am satisfied that the education I invested in with my student loan(s) was worth the investment for personal growth." 70.6% agreed.

( ____ , _____ )

,
Conclusion

____While many feel that loans are a burden and wish they had borrowed less, a minority are satisfied with their education.

____While many feel that loans are a burden and wish they had borrowed less, a majority are satisfied with their education.

____While a minority feel that loans are a burden and wish they had borrowed more, a minority are satisfied with their education.

____While a minority feel that loans are a burden and wish they had borrowed more, a majority are satisfied with their educatio

THANK YOU

To what extent do syntax textbooks, which analyze the structure of sentences, illustrate gender bias? A study of this question sampled sentences from 10 texts. One part of the study examined the use of the words "girl," "boy," "man," and "woman." We will call the first two words juvenile and the last two adult. Is the proportion of female references that are juvenile (girl) equal to the proportion of male references that are juvenile (boy)? Here are data from one of the texts:

Gender	n	X(juvenile)
Female	63	48
Male	134	50

(a) Find the proportion of juvenile references for females and its standard error. Do the same for the males. (Round your answers to three decimal places.)

Answers:

p̂F	=
SEF	=
p̂M	=
SEM	=

(b) Give a 90% confidence interval for the difference. (Do not use rounded values. Round your final answers to three decimal places.)

( ______ , _____ ) Answers

(c) Use a test of significance to examine whether the two proportions are equal. (Use p̂_F − p̂_M. Round your value for z to two decimal places and round your P-value to four decimal places.)

Answers :

z	=
P-value	=

State your conclusion.

___There is not sufficient evidence to conclude that the two proportions are different.

___There is sufficient evidence to conclude that the two proportions are different.    

THANK YOU :)

Statistics Question

Data provided below

(To be done with EVIEWS or any other data processor)

d)

e) In general, we can conduct hypothesis tests on a population central location with EViews by performing the (one sample) t-test, the sign test or the Wilcoxon signed ranks test.2 Suppose we would like to know whether there is evidence at the 5% level of significance that the population central location of NAR is larger than 5%. which test(s) offered by EViews would be the most appropriate this time? Explain your answer by considering the conditions required by these tests.

(f) Perform the test you selected in part (e) above with EViews. Do not forget to specify the null and alternative hypotheses, to identify the test statistic, to make a statistical decision based on the p-value, and to draw an appropriate conclusion. If the test relies on normal approximation, also discuss whether this approximation is reasonable this time.

(g) Perform the other tests mentioned in part (e). Again, do not forget to specify the null and alternative hypotheses, to identify the test statistics, to make statistical decisions based on the p-values, and to draw appropriate conclusions. Also, if the tests rely on normal approximation, discuss whether these approximations are reasonable this time.

(h) Compare your answers in parts (f) and (g) to each other. Does it matter in this case whether the population of net returns is normally, or at least symmetrically distributed or not? Explain your answer.

PURCHASE	NAR
Direct	9.33
Direct	6.94
Direct	16.17
Direct	16.97
Direct	5.94
Direct	12.61
Direct	3.33
Direct	16.13
Direct	11.20
Direct	1.14
Direct	4.68
Direct	3.09
Direct	7.26
Direct	2.05
Direct	13.07
Direct	0.59
Direct	13.57
Direct	0.35
Direct	2.69
Direct	18.45
Direct	4.23
Direct	10.28
Direct	7.10
Direct	3.09
Direct	5.60
Direct	5.27
Direct	8.09
Direct	15.05
Direct	13.21
Direct	1.72
Direct	14.69
Direct	2.97
Direct	10.37
Direct	0.63
Direct	0.15
Direct	0.27
Direct	4.59
Direct	6.38
Direct	0.24
Direct	10.32
Direct	10.29
Direct	4.39
Direct	2.06
Direct	7.66
Direct	10.83
Direct	14.48
Direct	4.80
Direct	13.12
Direct	6.54
Direct	1.06
Broker	3.24
Broker	6.76
Broker	12.80
Broker	11.10
Broker	2.73
Broker	0.13
Broker	18.22
Broker	0.80
Broker	5.75
Broker	2.59
Broker	3.71
Broker	13.15
Broker	11.05
Broker	3.12
Broker	8.94
Broker	2.74
Broker	4.07
Broker	5.60
Broker	0.85
Broker	0.28
Broker	16.40
Broker	6.39
Broker	1.90
Broker	9.49
Broker	6.70
Broker	0.19
Broker	12.39
Broker	6.54
Broker	10.92
Broker	2.15
Broker	4.36
Broker	11.07
Broker	9.24
Broker	2.67
Broker	8.97
Broker	1.87
Broker	1.53
Broker	5.23
Broker	6.87
Broker	1.69
Broker	9.43
Broker	8.31
Broker	3.99
Broker	4.44
Broker	8.63
Broker	7.06
Broker	1.57
Broker	8.44
Broker	5.72
Broker	6.95

Suppose that you roll a die and your score is the number shown on the die. On the other
hand, suppose that your friend rolls five dice and his score is the number of 6’s shown out of five rollings. Compute the probability
(a) that the two scores are equal.
(b) that your friend’s score is strictly smaller than yours.

. A chemist wishes to detect an impurity in a certain compound that she is making. There is a test that detects an impurity with probability 0.92; however,

This test indicates that an impurity is there when it is not about 5% of the time. The chemist produces compounds with the impurity about 15% of the time. A compound is selected at random from the chemist’s output. The test indicates that an impurity is present. What is the conditional probability that the compound actually has the impurity?