When doing regression, simple linear or any of the other regression approaches, the analyst always must begin with the determination/isolation of at least two key variables -- one "dependent" and the other "independent". So, for example, I may do a forecast of future profits that relies on sales data (independent) and associated profit data (dependent) from the same years. We say something like...

"Since profits "depend" on sales volume (not the other way around), we can use one (sales) to forecast the other (profit)."

Find an example of a regression model with Google. Then explain which variables used in the model are "dependent" vs. "independent."

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. Santa Fe black-on-white is a type of pottery commonly found at archaeological excavations at a certain monument. At one excavation site a sample of 610 potsherds was found, of which 350 were identified as Santa Fe black-on-white.

(a) Let p represent the proportion of Santa Fe black-on-white potsherds at the excavation site. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 95% confidence interval for p. (Round your answers to three decimal places.) lower limit upper limit Give a brief statement of the meaning of the confidence interval. 95% of the confidence intervals created using this method would include the true proportion of potsherds. 5% of all confidence intervals would include the true proportion of potsherds. 95% of all confidence intervals would include the true proportion of potsherds. 5% of the confidence intervals created using this method would include the true proportion of potsherds.

(c) Do you think that np > 5 and nq > 5 are satisfied for this problem? Explain why this would be an important consideration. Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal. Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial. No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial. No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.

Bob Nale is the owner of Nale’s Quick Fill. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. Assume the number of gallons sold follows the normal distribution with a population standard deviation of 2.00 gallons. From his records, he selects a random sample of 65 sales and finds the mean number of gallons sold is 9.10.

What is the point estimate of the population mean?

Develop a 98% confidence interval for the population mean. (Use z Distribution Table.)

SPC Project

A small electronic device is designed to emit a timing signal of 200 milliseconds (ms) duration. In the production of this device, 20 samples of five units are taken and tested. and R are calculated for each sample and used to plot control charts. The results are shown in the following table.

a. Compute the averages, upper control limits, and lower control limits for and R charts for this data. Use the equations on pages 194-195 of your text, and Table 6.1 (page 195) for A2, D3, and D4.

b. Plot the R and charts in Excel. Is the process in statistical control?

c. Estimate the standard deviation of the process (σ) from the range data. σ = /d2, where d2 = 2.326 for a sample size of 5.

d. Assuming that the distribution of the data is approximately normal, what proportion of the devices would you expect to meet specifications of Lower Specification Limit = 190.5 and Upper Specification Limit = 210.5? Use the estimate of the standard deviation you calculated in part c.

Let Y denote a random variable that has a Poisson distribution with mean λ = 3. (Round your answers to three decimal places.)

(a) Find P(Y = 6)

(b) Find P(Y ≥ 6)

(c) Find P(Y < 6)

(d) Find P(Y ≥ 6|Y ≥ 3).

In the video, studies of twins were used to add evidence to a debate about whether an individual's character is formed primarily from their genetics or their environment. Review your course readings and answer the following questions related to the Nature or Nurture debate

In your own words, explain how the use of twin studies can help to clarify whether characteristics are determined primarily by genes or environment.

The assumption made in this debate is that factors in an individual’s genetic make-up, or in their environment, cause how they act as adults. Discuss whether you agree with that assumption and why or why not.

In your opinion, does the high degree of correlation between the behavior of twins prove that genetics causes their behavior?

Why might you question how well one variable predicts another, such as whether genes or environment predicts adult behavior?

Thinking about your own life experiences, describe reasons why your genetics or childhood environment might fail to predict your current decisions and actions.

Is college worth it? Among a simple random sample of 344 American adults who do not have a four-year college degree and are not currently enrolled in school, 166 said they decided not to go to college because they could not afford school.

1. Calculate a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it, and interpret the interval in context. Round to 4 decimal places.

2. Suppose we wanted the margin of error for the 90% confidence level to be about 2.25%. What is the smallest sample size we could take to achieve this? Note: For consistency's sake, round your z* value to 3 decimal places before calculating the necessary sample size.

choose n=

Choice blindness is the term that psychologists use to describe a situation in which a person expresses a preference and then doesn't notice when they receive something different than what they asked for. The authors of the paper "Can Chocolate Cure Blindness? Investigating the Effect of Preference Strength and Incentives on the Incidence of Choice Blindness"† wondered if choice blindness would occur more often if people made their initial selection by looking at pictures of different kinds of chocolate compared with if they made their initial selection by looking at the actual different chocolate candies.

Suppose that 200 people were randomly assigned to one of two groups. The 100 people in the first group are shown a picture of eight different kinds of chocolate candy and asked which one they would like to have. After they selected, the picture is removed and they are given a chocolate candy, but not the one they actually selected. The 100 people in the second group are shown a tray with the eight different kinds of candy and asked which one they would like to receive. Then the tray is removed and they are given a chocolate candy, but not the one they selected.

If 22 of the people in the picture group and 13 of the people in the actual candy group failed to detect the switch, would you conclude that there is convincing evidence that the proportion who experience choice blindness is different for the two treatments (choice based on a picture and choice based on seeing the actual candy)? Test the relevant hypotheses using a 0.01 significance level. (Let p₁ be the proportion who experience choice blindness based on a picture treatment, and p₂ be the proportion who experience choice blindness based on seeing the actual candy treatment.)

Find the test statistic and p-value.

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?