A laptop assembly is subjected to a final functional test. Suppose that defects occur at random in these assemblies, and that defects occur according to a Poisson distribution with parameter λ= 0.03.

1. What is the probability that an assembly will have exactly one defect?
2. What is the probability that an assembly will have one or more defects?
3. What is the probability that an assembly will have no more than three defects?
4. What is the probability that an assembly will have more than two defects?
5. Suppose that you improve the process so that the occurrence rate of defects is cut in half to λ = 0.015. What effect does this have on the probability that an assembly will have one or more defects?

The diameter of a brand of tennis balls is approximately normally​ distributed, with a mean of 2.58 inches and a standard deviation of 0.03 inch. A random sample of 11 tennis balls is selected.

The probability is 69% that the sample mean will be between what two values symmetrically distributed around the population​ mean? (Round to two decimal places).

The lower bound is ___ inches, the upper bound is ___ inches.

Scenario: Imagine that a psychologist working with veterans with post-traumatic stress disorder wants to compare the effectiveness of several therapies focused on reducing symptoms of anxiety. The psychologist randomly sampled 20 veterans who recently returned from combat and randomly assigned each of them to receive one of four interventions for 8 weeks. A survey was used to measure the participants’ anxiety at the end of the 8 weeks. Higher anxiety scores indicate more anxiety.

Use SPSS to compare the mean anxiety scores with a one-way ANOVA.

1. Before computing any analyses, state the null hypothesis and alternative hypothesis in words (not formulas).
2. Identify the factor and dependent variable.
3. Name the levels of the factor.
4. State the degrees of freedom between groups and explain how you calculated it by hand.
5. State the degrees of freedom within groups and explain how you calculated it by hand.
6. Identify the obtained F value using SPSS and report it in your answer document.
7. Identify the p value using SPSS and report it in your answer document.
8. Explain whether the F test is statistically significant. Explain how you know.
9. Explain what the psychologist can conclude about the relationship between different types of therapy and anxiety.
10. Should the psychologist conduct a post hoc test? Why or why not? If post hoc testing is needed, conduct a Tukey HSD post hoc analysis in SPSS. Explain what the results tell you.

The ages of a random sample of people who attended a recent soccer match are as follows:

23 35 14 37 38 15 45

12 40 27 13 18 19 23

37 20 29 49 40 65 53

18 17 23 27 29 31 42

35 38 22 20 15 17 21

a. Find the mean age.

b. Find the standard deviation.

c. Find the coefficient of variation.

An exam has 5 questions and each of them has 4 possible answers. A student gets 3 points
for each correct answer and loses 1 point for each wrong answer. Consider a student who
answers all questions completely at random. Let X denote the number of correct answers and
Y the number of points of this student at the end of the test. (A negative score is possible).
(a) Compute the mean and the standard deviation of Y , µY and σY .
(b) Compute P(µY − σY ≤ Y ≤ µY + σY ) and P(µY − 2σY ≤ Y ≤ µY + 2σY ).
(c) What is the probability that the student above gets a positive score?

Graphically speaking, what happens to the slope of an objective function if a coefficient in the objective function is changed?

City Mileage, Highway Mileage. We expect a car's highway gas mileage to be related to its city gas mileage (in miles per gallon, mpg). Data for all 1137 vehicles in the government's 2013 Fuel Economy Guide give the regression line

highway mpg = 6.785 + (1.033 x city mpg)

for predicting highway mileage from city mileage.

(a) What is the slope of this line? Say in words what the numerical value of the slope tells you.

(b) What is the intercept? Explain why the value of the intercept is not statistically meaningful.

(c) Find the predicted highway mileage for a car that gets 16 miles per gallon in the city. Do the same for a car with city mileage of 28 mpg.

Four important measurements were taken in harsh environmental conditions. Two of the four measurements were lost in the harsh conditions and the remaining two are

5       3

However a scientist recalls the mean and variance of the four measurements were 6 and 20/3, respectively. Find the two missing measurements.

for this problem. At least four digits after the decimal in your calculations answers May Vary slightly due to rounding a random sample of 5100 permanent dwellings on an entire reservation show that 1585 for traditional Hogan's let P be the proportion of all permanent dwellings on the entire reservation that are traditional Hogan's find a point estimate for p round your answer answer to four decimal places B find a 99% confidence interval for p round your answer to three decimal places upper and lower limits give a brief interpretation of the confidence interval see do you think the NP is greater than 5 and nq greater than 5 or satisfied for this problem explain why this would be an important consideration

In the past, 30% of a country club's members brought guests to play golf sometime during the year. Last year, the club initiated a new program designed to encourage members to bring more guests to play golf. In a sample of 80 members, 29 brought guests to play golf after the program was initiated. Therefore, the test statistic is 1.22. When testing the hypothesis that the new program has increased the proportion of members bringing out guests (using a 5% level of significance), what is the p-value? (please round your answer to 4 decimal places)

1. Calculate the weighted unit cost per square foot for the project data shown below, and determine the cost of a 30,000-sf project.








2. Determine the relationship between unit cost and size for the project data above, and use it to estimate the cost of a 25,000-sf project.

3. Use the time and location indices presented during Class10 to estimate the cost of a building that contains 48,000 sf of floor area. The building is to be constructed 3 years from now in City C. The cost of a similar type of building that contained 32,000 sf was completed 2 years ago in City B for a cost of $3,680,000.
Project Total Cost Size, sf 1 $ 3,036,400 26,400 2 $ 3,129,700 29,800 3 $ 2,580,300 21,500 4 $ 2,287,500 18,300 5 $ 2,743,200 23,450 6 $ 3,065,300 32,350 7 $ 4,503,600 41,700

1. You are given with the regression result that shows the regression model with k variables. Answer the following parts:

a) How do you tell that a certain variable is influential?

b) Suppose the theoretical issue said there exist a linear constraint, how do you figure out the constraint holds?

c) Suppose you have two sets of explanatory variables; how did you consider which set is the better one?

d) What’s the meaning of R-squared? Should we always look for the model that has the high R-squared?

e) Suppose the explanatory variables are subject to linear dependence among themselves, what is the correct procedure to estimate the coefficients?

You flip a coin, if it is heads you will have a good day and if it is tails you will have a bad day. There are 30 days in total.

(a) What is the expectation and variance of the number of times you will have a good day throughout this 30 day stretch?

(b) What is the probability that every day will be bad for all of the 30 days?