An article reported that for a sample of 56 kitchens with gas cooking appliances monitored during a one-week period, the sample mean CO2 level (ppm) was 654.16, and the sample standard deviation was 162.

(a) Calculate and interpret a 95% (two-sided) confidence interval for true average CO2 level in the population of all homes from which the sample was selected. (Round your answers to two decimal places.) , ppm

(b) Suppose the investigators had made a rough guess of 183 for the value of s before collecting data. What sample size would be necessary to obtain an interval width of 49 ppm for a confidence level of 95%? (Round your answer up to the nearest whole number.)

A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows:

a. Find the sample regression equation for the model: Salary = β₀ + β₁Education + ε. (Round answers to 3 decimal places.)

Salaryˆ=Salary^=    +   Education

b. Interpret the coefficient for Education.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $8,590.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $7,161.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $8,590.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $7,161.

c. What is the predicted salary for an individual who completed 6 years of higher education? (Round answer to the nearest whole number.)

SalaryˆSalary^               $

A hotel wanted to develop a new system for delivering room service breakfasts. In the current system, an order form is left on the bed in each room. If the customer wishes to receive a room service breakfast, he or she places the order form on the doorknob before 11p.m. The current system requires customers to select a 15-minute interval for desired delivery time (6:30~6:45a.m., 6:45~7:00a.m., etc.). The new system is designed to allow the customer to request a specific delivery time. The hotel wants to measure the difference (in min.) between the actual delivery time and the requested delivery time of room service orders for breakfast (negative time means that the order was delivered before the requested time, whereas the positive time means that the order was delivered after the requested time). The factor included were the menu choice (American and Continental) and the desired time period in which the order was to be delivered (Early Time Period [6:30~8:00a.m.] or Late Time Period[8:00~9:30a.m.]). Ten orders for each combination of menu choice and desired time period were studied on a particular day, and the data were stored

(a) At the 0.05 level of significance, is there an interaction between type of breakfast and desired time?

(b) Draw the plot of means.

(c) At the 0.05 level of significance, is there an effect due to type of breakfast?

(d) At the 0.05 level of significance, is there an effect due to desired time?

A producer of a variety of salty snacks would like to estimate the average weight of a bag of BBQ potato chips produced during the filling process at one of its plants. Determine the sample size needed to construct a 99​% confidence interval with a margin of error equal to 0.007 ounces. Assume the standard deviation for the potato chip filling process is 0.05 ounces.

The sample size needed is______________​(Round up to the nearest​ integer.)

_____________________________________________________________________________________________________________________________________

Determine the sample size needed to construct a 95%confidence interval to estimate the average GPA for the student population at a college with a margin of error equal to 0.2. Assume the standard deviation of the GPA for the student population is 2.5.

The sample size needed is________________​(Round up to the nearest​ integer.)

1.

a. In hypothesis testing when is a two-tail test used in lieu of a one-tail test and why?

b. In hypothesis testing when is the "t test" used rather than the "Z test"?

2.

a. If the question asks "is there evidence that the average price of gas is greater than some value ‘A’ is this a one-tail or two-tail test and why? What would your null and alternative hypothesis be and why?

b. What is the distinction between a Type 1 error and a Type 2 error?

Substances to be tested for cancer-causing potential are often painted on the skin of mice. The question arose whether mice might get an additional dose of the substance by licking or biting their cagemates. To answer this question, the compound benzo(a)pyrene was applied to the backs of 10 mice: 5 were individually housed, and 5 were group-housed in a single cage. After 48 hours, the concentration of the compound in the stomach tissue of each mouse was determined. The results (nmol/gm) were as follows:

Carry out the calculations required to compare the two groups using a Wilcoxon rank sum test. State the null and alternative hypotheses for the appropriate one-sided test. Calculate the test statistic. Using the function pwilcox() in R, calculate the p-value corresponding to this statistic. Assuming the desired Type I error level is 0.05, do these data provide enough evidence to reject the null hypothesis?

The data set contains the compressive strength, in thousands of pounds per square inch (psi), of 30 samples of concrete taken two and seven days after pouring.

(a) At the 0.10 level of significance, is there evidence of a difference in the mean strengths at two days and at seven days?

(b) Find the p-value in (a) and interpret its meaning.

(c) At the 0.10 level of significance, is there evidence that the mean strength is lower at two days than at seven days?

(d) Find the p-value in (c) and interpret its meaning.

A tire manufacturer produces tires that have a mean life of at least 30000 miles when the production process is working properly. The operations manager stops the production process if there is evidence that the mean tire life is below 30000 miles.

The testable hypotheses in this situation are H0:μ=30000H0:μ=30000 vs HA:μ<30000HA:μ<30000.

1. Identify the consequences of making a Type I error.
A. The manager stops production when it is not necessary.
B. The manager stops production when it is necessary.
C. The manager does not stop production when it is not necessary.
D. The manager does not stop production when it is necessary.

2. Identify the consequences of making a Type II error.
A. The manager stops production when it is necessary.
B. The manager does not stop production when it is necessary.
C. The manager does not stop production when it is not necessary.
D. The manager stops production when it is not necessary.

To monitor the production process, the operations manager takes a random sample of 30 tires each week and subjects them to destructive testing. They calculate the mean life of the tires in the sample, and if it is less than 29000, they will stop production and recalibrate the machines. They know based on past experience that the standard deviation of the tire life is 2750 miles.

3. What is the probability that the manager will make a Type I error using this decision rule? Round your answer to four decimal places.

4. Using this decision rule, what is the power of the test if the actual mean life of the tires is 28750 miles? That is, what is the probability they will reject H0H0 when the actual average life of the tires is 28750 miles? Round your answer to four decimal places.

1) Distinguish between Time Series models and Causal models. The different types of control charts and reasons for their use. Provide a working example of each in the auto manufacturing industry.

2) Discuss each of the basic patterns mentioned by the authors for Time Series Models. Provide an example of each.

3) Distinguish between Simple Moving Average and Weighted Moving Average. What are their benefits and how are these applied in the real world?

4) Distinguish between low and high α values and what they represent in Exponential Smoothing.

5) Distinguish between linear regression and correlation. Provide a working example of each in business.

You’re waiting for Caltrain. Suppose that the waiting times are approximately Normal with a mean of 12 minutes and a standard deviation of 3 minutes. Use the Empirical Rule to estimate each of the following probabilities without using the normalcdf function of your calculator:

a) What is the probability that you’ll wait between 9 and 15 minutes for the train?

b) What is the probability that you’ll wait between 6 and 18 minutes for the train?

c) What is the probability that you’ll wait between 3 and 21 minutes for the train?

d) What is the probability that you’ll wait more than 12 minutes for the train?

e) What is the probability that you’ll wait between 12 and 18 minutes for the train?

f) What is the probability that you’ll wait between 3 and 18 minutes for the train?

g) What is the probability that you’ll wait more than 21 minutes for the train?

Please show your work.

A. If a normal distribution of scores has a mean of 100 and a standard deviation of 10, what percentage of scores would lie below 70? a. 0.13%. b.2.15%. c. 2.28% d. 99.87%

B. What percentage of scores lie between 85 and 100 for a normal distribution with a mean of 100 and a standard deviation of 15? a. +15% b.-15% c.34.13% d. -34.13%

C What percentage of scores lie between 70 and 80 for a normal distribution with the mean of 100 and a standard deviation of 10? a.+27% b.-13% c.-7%. d. 2.15%.

Iconic memory is a type of memory that holds visual information for about half a second (0.5 seconds). To demonstrate this type of memory, participants were shown three rows of four letters for 50 milliseconds. They were then asked to recall as many letters as possible, with a 0-, 0.5-, or 1.0-second delay before responding. Researchers hypothesized that longer delays would result in poorer recall. The number of letters correctly recalled is given in the table.

(a) Complete the F-table. (Round your values for MS and F to two decimal places.)

(b) Compute Tukey's HSD post hoc test and interpret the results. (Assume alpha equal to 0.05. Round your answer to two decimal places.)

The critical value is for each pairwise comparison.

Which of the comparisons had significant differences? (Select all that apply.)

Recall following no delay was significantly different from recall following a one second delay. The null hypothesis of no difference should be retained because none of the pairwise comparisons demonstrate a significant difference. Recall following no delay was significantly different from recall following a half second delay. Recall following a half second delay was significantly different from recall following a one second delay.

The number of chocolate chips in a an 18-ounce bag of Chips Ahoy! Chocolate chip cookies is approximately normally distributed, with a mean of 1262 chips and a standard deviation of 118 chips, according to a study by cades of the US Air Force Academy.

1. What proportion of 18 ounce bags has more than 1000 chips?

On a multiple choice examination, each question has exactly five options, of which the student must pick one. Only one option is correct for each question. If the student is merely guessing at the answer, each option should be equally likely to be chosen. Given that the test has 18 questions, and that a student is just guessing on each question, find the probability of the following events: (a) exactly three are correct, (b) fewer than five are correct, (c) between two and sever answers are correct.