1. Complete the problems below.

a. Find the critical value z a/2 that corresponds to 93% confidence level.

Z a/2 = _____

Q1 (ROUND TO 2 DECIMAL PLACES)

b.You plan to conduct a survey to estimate the percentage of people who eat breakfast. Find the number of people who must be surveyed if you want to be 93% confident that the sample percentage is within two percentage points of the true population percentage.

(USE YOUR ANSWER FROM PROBLEM #1a for critical values)

Assume that nothing is known about the percentage to be estimated. n=__________Q2

Assume that studies have shown that 34% of the people eat breakfast. n=___________Q3

c.

In a survey of 1002 people, 701 said they voted in a recent presidential election. Construct a 95% confidence interval for the proportion of people who said they voted in a recent presidential election.

(ROUND TO 3 DECIMAL PLACES)

Confidence Interval ( ___________________Q4 , ___________________Q5)

The Environmental Protection Agency has determined that safe drinking water should, on average, contain no more than

1.3 mg/liter of copper. You are testing water from a new source, and take 31 water samples. The mean copper content in

your samples is 1.46 mg/l and the standard deviation is 0.18 mg/l.

(a) Is there convincing evidence at the α = 0.05 significance level that the water from this source contains unsafe levels of

copper? (Do a 4-step process)

(b) Referring to your conclusion, what type of error may have been made? Describe the error in the context of this study.

(c) Describe two ways to increase the power of the test in part (a).

A cost estimator for a construction company has collected the data found in the source file Estimation.xlsx describing the total cost (Y) of 97 difference projects and the following 3 independent variables thought to exert relevant influence on the total cost: total units of work required (X1), contracted units of work per day (X2), and city/location of work (X3). The cost estimator would like to develop a regression model to predict the total cost of a project as a function of these 3 independent variables.

b. Suppose the estimator wants to use the total units of work required (X1), contracted units of work per day (X2), and city/location of work (X3) as the independent variables to predict total cost. What should be the regression function between Y and X1, X2, and X3? What is the adjusted R-squared value of this model? What conclusions can you make? (Note that X3 is a dummy variable. You should process it into different categories as I showed you in the class lecture. You should expand X3 into Location1, Location 2, …. Location 5 to differentiate the six locations.)

The union for a particular industry has determined that the standard deviation of the daily wages of its workers is $19. A random sample of 70 workers in this industry has a mean daily wage of $117. Find a 90% confidence interval for the true mean daily wage of all union workers in the industry. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.

Recorded here are the germination times (in days) for sixteen randomly chosen seeds of a new type of bean: 11, 13, 12, 13, 20, 15, 18, 17, 14, 18, 10, 12, 13, 17, 14, 17 Send data to Excel Assuming that germination times are normally distributed, find a 95% confidence interval for the mean germination time for all beans of this type. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.) What is the lower limit of the confidence interval? What is the upper limit of the confidence interval?

Valles Global Industries (VGI) is getting ready to market their Internet-based party planning service. One of the menu items is a kabob. The kabob was designed to have four vegetable chunks and three chunks of protein: beef, chicken, shrimp or tofu. On average, any vegetable will yield 5 chunks suitable for a kabob. One of any ten vegetables will be of poor quality and cannot be used. In presenting a menu and budget to a party-thrower, VGI recommends two kabobs per person.

1. VGI also offers a statistical modeling program that prevents food waste. They have data that recommends a mean number of party attenders as well as metrics on variability. Imagine you are planning an event with VGI. They suggest the number of party-attenders for a 200 person party estimate is actually distributed N(150, 1225). They also recommend using a probability of 90 percent for attendees. If VGI charges you $100 per attendee, how much does their recommendation save you?
2. Referring to A above, would you take their recommendation? Why or why not?

A certain virus infects one in every

150

people. A test used to detect the virus in a person is positive

80%

of the time when the person has the virus and

55​%

of the time when the person does not have the virus.​ (This

55​%

result is called a false

positive​.)

Let A be the event​ "the person is​ infected" and B be the event​ "the person tests​ positive."

​(a) Using​ Bayes' Theorem, when a person tests​ positive, determine the probability that the person is infected.

​(b) Using​ Bayes' Theorem, when a person tests​ negative, determine the probability that the person is not infected.

Members of the millennial generation are continuing to be dependent on their parents into early adulthood. A family research organization has claimed that, in past generations, no more than 27% of individuals aged 18 to 32 continued to be dependent on their parents. Suppose that a sample of 350 individuals aged 18 to 32 showed that 132 of them continue to be dependent on their parents.

1. Develop hypothesis for a test to determine whether the proportion of millennial continuing to be dependent on their parents is higher than for past generations.

2. What is your point estimate of the proportion of millennial continuing to be dependent on their parents?

3. What is the p-value provided by sample data?

4. What is your hypothesis testing conclusion? Use a=.05 as level of significance.

6.

A survey of 25 grocery stores produced the following sample statistics: 1.) mean price for a gallon of milk was $2.98, and 2.) a calculated standard error of $0.10. What is the 98% confidence interval to estimate the true cost of a gallon of milk?

Multiple Choice

• $2.73 to $3.23

• $2.85 to $3.11

• $2.94 to $3.02

• $2.95 to $3.01

7.

The z-score or z-value corresponding to a 95.34% confidence interval is ______.

Multiple Choice

• 1.96

• 1.65

• 1.99

• 1.68

8. The level of significance is the probability of rejecting the null hypothesis when it is actually true.

True or False

9. A test statistic is a value, determined from sample information, used to decide whether to reject the null hypothesis.

True or False

10. If the null hypothesis is µ ≥ 200, then a two-tail test is being conducted.

True or False

. According to a 2018 report from the Center on Education and the Workforce at Georgetown University, 70 percent of full-time college students are working. Suppose 15 students full-time college students are randomly selected and asked whether they are working. (a) (3 points) Explain (as best as you can) why this is a binomial experiment.

(b) (1 points) Find and interpret the probability that exactly 10 students say they work. (c) (1 points) Find and interpret the probability that at least 10 students say they work. (d) (2 points) Find the expected value and the standard deviation of this binomial random variable. (e) (2 points) Which event is more likely, A) at most 11 students work or B) 14 or more students work ? How do you know?

Consider the following data of experimental data measuring the lifetime of a wire as a function of temperature

1. Sketch scatter plots of untransformed data and of ln(lifetime) vs 1/temp

2. Estimate the lifetime of the wire at t=230 using the better model, be it untransformed or transformed.

4. Customers enter a store at a rate of 3 customers per hour.

a) Compute the probability that at least two, but no more than five customers enter the store in a given hour.

b) Compute the probability that it takes more than 30 minutes for the first customer to enter the store this hour.

c) Suppose you know that exactly 1 customer entered the store during a given hour. Compute the probability that the customer entered the store between minute 10 and minute 30.

d) Let Xk be the number of customers that enter a store during hour k. Suppose you recorded how many customers entered the store each hour for the last 60 hours. What is the approximate distribution of X¯? Make sure to specify the parameter(s) of the distribution.

Give an example of a hypothesis test problem for either a proportion or a mean and describe the parts of the problem which identify the hypothesis test as working with a proportion or mean. State which calculator feature is used with the problem. 50 words

Use the International Stock Market database from “Excel Databases.xls” on Blackboard. Use Excel to develop a multiple regression model to predict the DJIA by the Nasdaq, the S&P 500, the Nikkei, the Hang Seng, the FTSE 100, and the IPC. Performing a stepwise regression analysis at a 5% level of significance, add the independent variable from Step 2 and continue to perform the stepwise regression analysis until you have reached the best linear model. Which independent variables are in the best linear model? Check all that apply.

Excel Data Here

https://drive.google.com/file/d/1TQG5r2wzLGk--75whZXyb0SDTHZTWS0S/view?usp=sharing

A: Nasdaq

B: S&P 500

C: Nikkei

D: Hang Seng

E: FTSE 100

F: IPC

Choose All Answers That Apply

4. Does distance from object affect the eye focus time? An industrial engineer is conducting an experiment on eye focus time. She is interested in the effect of the distance of the object from the eye on the focus time. Four distances (4’, 6’, 8’, 10’) will be studied. She has 5 subjects available for the experiment, and has decided that she will test each subject at each of the 4 distances; the order in which the distances are tested will be randomly decided for each study participant. The focus time measurements are given in the table below and are posted on in a text file Eyedata.

2

(a) What type of experimental design was used in this experiment?

(b) What statistical model would you use to analyze these data?

(c) What assumptions would be required for the model in (b)?

(d) What evidence do these data provide for / against the hypothesis that the distance has no effect on focus time?

(e) What contrast would you use to test for a difference between the mean focus times for distances of 4’ and 6’? Find a 95% confidence bound for this contrast and interpret.

(f) Test if there is a significant difference between the 4’ and 6’ group with the 8’and 10’ group. Clearly state the contrast you will use, find its unbiased estimator and standard error of the estimator. Next perform the test.

Subject Distance FocusTime

1 4 10

2 4 6

3 4 6

4 4 6

5 4 6

1 6 7

2 6 6

3 6 6

4 6 1

5 6 6

1 8 5

2 8 3

3 8 3

4 8 2

5 8 5

1 10 6

2 10 4

3 10 4

4 10 2

5 10 3