The following partial ANOVA table was based on an experiment performed as a two-factor design with 2 levels of factor A, 3 levels of factor B, and 5 observations on each treatment. It was determined that treatment groups were independently selected from a normal distribution with the same variance for each treatment.

a) Fill in the missing entries in the ANOVA table.

b) Test the hypothesis of no interaction between the factors at a 5% level of significance. Your answer should show assumptions, hypotheses, and conclusions.

c) Indicate whether testing for the main effects is appropriate, and if so show, the results of the tests; if not, indicate why testing for the main effects is not justified. Your answer should show assumptions, hypotheses, and conclusions.

A questionnaire collects information from UTS students on gender and whether or not the student smokes. The resultant two-way table is shown below.

Women Men Total

Don’t smoke 153 166 319

Smoke 16 27 43

Total 169 193 362

a) We intend to test whether there is a difference in the proportion of men and women who smoke. Define the parameters, and state the Null and Alternative hypotheses

b) What proportion of men are smokers? What proportion of women are smokers? What is the difference between these proportions?

c) Using information associated with the plots on the next page o Which plot would you use to perform the test in part a)? o Let = 0.05, State your conclusion about whether there is a difference in the proportion of men and women who smoke - with a numerical reference from the appropriate plot

The fuel efficiency, measured in miles per gallon, was measured for each of 12 cars when the cars where brand new. After exactly 5 years of use, the fuel efficiency of the same 12 cars was measured again. The data is in the following table. Mileage when New Mileage after 5 years Difference 16 15 1 27 24 3 17 17 0 33 29 4 28 25 3 24 22 2 18 16 2 22 20 2 20 21 -1 22 20 2 29 22 7 21 22 -1 a). Construct a 99% CI for the mean difference between initial fuel efficiency and the fuel efficiency after 5 years. b). Do the data give an evidence that there is no difference in fuel efficiency.

The following data was collected to explore how the average number of hours a student studies per night and the student's GPA affect their ACT score. The dependent variable is the ACT score, the first independent variable (x1) is the number of hours spent studying, and the second independent variable (x2) is the student's GPA.

Copy Data

part 1:  

Find the p-value for the regression equation that fits the given data. Round your answer to four decimal places.

Part 2: find if a statistically significant relationship exists between the independent and dependent variables at .01 level of significance. Round to 3 decimal plaes. (ie. y= _+_x1+_x2, or not enough evidence)

The null and alternate hypotheses are: H0 : μ1 = μ2 H1 : μ1 ≠ μ2 A random sample of 9 observations from one population revealed a sample mean of 22 and a sample standard deviation of 3.9. A random sample of 9 observations from another population revealed a sample mean of 27 and a sample standard deviation of 4.1. At the 0.01 significance level, is there a difference between the population means? State the decision rule. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) The decision rule is to reject HO if T< or t> . b) Compute the pooled estimate of the population variance. (Round your answer to 3 decimal places.) Pooled estimate of the population variance=? Compute the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) Test Statistic=?

You are interested in finding a 90% confidence interval for the mean number of visits for physical therapy patients. The data below show the number of visits for 13 randomly selected physical therapy patients. Round answers to 3 decimal places where possible. 19 19 14 13 26 19 5 14 17 27 13 20 28 a. To compute the confidence interval use a distribution. b. With 90% confidence the population mean number of visits per physical therapy patient is between and visits. c. If many groups of 13 randomly selected physical therapy patients are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of visits per patient and about percent will not contain the true population mean number of visits per patient

The data are the ages of criminals and their victims.

1. Is there a significant correlation between the ages of the victims and the criminals? Provide support for your answer, and indicate the strength and direction of the correlation.
2. Conducting a simple linear regression, do they data support that a prediction of victim age can be obtained given the data provided in the file? Cite the elements of the output you used to draw your conclusion.
3. What is the equation of the regression, and what does that tell us?
4. How do correlation and regression differ?

Psychopaths tend to be cold and calculated, often not worrying about others or consequences so they are typically not anxious. You are curious whether anxiety scores for people are associated with psychopathy scores. To test this you survey 12 undergraduate students on their anxiety level (0 to 100, higher mean more anxious) and their score on a standard psychopathy measure (0 to 40, higher score indicated a higher level of psychopathy). The data is as follows:

1) If you consider both variables to be interval, what is the correlation between anxiety and psychopathy scores?

1. List the strength and direction of the following correlations: r = .02 r = .53 r = -.89 2. Describe the difference between correlation and prediction (regression) analysis approaches? 3a. A regression model predicting the yearly salary (Y) for a teacher is predicted by years of experience(X). The analysis produces a constant of 38,000 and an intercept (slope) of 1,500. According to the model, what would be the salary of a teacher who has worked for 12 years? 3b. Additional variables are added to improve the model predicting annual teacher salary (Y). The model now includes years of experience (X1), number of awards (X2), and age (X3). The analysis produces a constant of 38,000, and the following slopes (x1 = 1,500, x2 = 5,000, x3 = .055). What would be the salary of a teacher who has worked for 5 years, won 2 awards, and is 27-years-old?

Assume you are given two resistors with resistances R₁=4.0 kΩ and R₂=6.0 kΩ and two capacitors with capacitances C₁=4.0 µF and C₂=6.0 µF.

a)      Calculate the equivalent resistances R_eq and the equivalent capacitance C_eq if the resistors are connected in series and the capacitors are connected in parallel.

b)      Now, use the R_eq and C_eq that you calculate in part (a) to construct an RC circuit. An emf of 27 V is applied across R_eq and C_eq to charge the capacitor. After C_eq is fully charged, the battery is removed at t=0. Calculate the potential difference across the C_eq after t= 12µs.

c)      If the resistor R₁ is made of iron wire with radius R= 3 mm, calculate the length of this wire. The resistivity of iron is ρ_iron= 9.68x10^-8 Ω.m.

d)      If the capacitance C₂ has square parallel-plates with the area A = 20 cm². Calculate the separation between plates.