Some researchers tested whether arthritis in dogs could be improved by supplementation with antioxidants and/or an aminosugar mixture (containing glucosamine and chondroitin). They gave combinations of these supplements (each a factor with two levels: treatment and control) to equal numbers of test subjects in a balanced factorial design. They tested the effects of these supplements on levels of inflammation using a factorial ANOVA. The ANOVA table from their output is copied below.                                                                               

> model<-aov(inflammation~as.factor(antioxidant)*as.factor(aminosugar))

> anova(model)

a) How many hypotheses did they test with this model?   

b) How many test subjects (i.e. replicates) did the researchers have?

c) Did the order in which antioxidant and aminosugar effects entered this model affect their significance? Why?   

d) Name a measure of model fit that can be used to compare the relative fit of different models, while taking into account the number of parameters in each?

e) The researchers simplified their model by removing the interaction term and the main effect of aminosugar. Fill in the table below with the values of their new model.   

> model2<-aov(inflammation~as.factor(antioxidant))

> ANOVA(model)

f) Did the significance of antioxidant change by removing the other terms, and if so, did it become more or less significant?

g) By how much did the overall model R² change (explain whether it increased, decreased or no change, as well as the amount)?    (show your working)   

Boneitis is in the news again: several cases have been reported in Miami, and more are soon to follow. In order to receive aid from the state government, the city of Miami has to provide a small amount of evidence that the prevalence of the disease (i.e., the proportion of Miami residents who have boneitis) is greater than 20%. City ocials took a random sample of 200 residents and found that 33.0% had been diagnosed with boneitis.

(a) (4 points) Perform a z-test at the 0.01 significance level to determine if this sample provides evidence that the prevalence of boneitis in Miami is greater than 20%. Be sure to state the null and alternative hypotheses, any calculator functions you use (including inputs and relevant outputs), and clearly state your conclusion in context.

(b) (3 points) Construct a 95% plus-two confidence interval for pˆ, the sample proportion of Miami residents with boneitis. Show your work, including any calculator functions you use, and be sure to round interval bounds properly.

Compounds in the saliva, hair and urine of pets may potentially trigger asthma in some patients. To test this hypothesis, some researchers conducted a study. As test subjects, they used 8 families, 4 of which had a pet in their home and 4 did not. They measured respiratory flow of each family member, as this is known to decrease in patients with asthma. Recent research has shown body weight to correlate with asthma in children, and sex, age, and height are also known to affect respiratory flow measures. Therefore, the researchers measured and included these covariates in their model to control for any confounding effects that they may have had before testing their treatment of interest (whether the home had pets). The analysis conducted by the researchers is presented below. They concluded that pets in the family do not influence respiratory flow.

> attach(pets.data)

> pets.data

resp.flow body.weight treatment sex age height family

1 266          41     pet   F 13    130 Smith

2 400          95     pet    M 37    190   Smith

3 369          81     pet    F 36    180   Smith

4 365          78     pet    M 42    185   Wilson

5 351          75     pet    M 35    192   Wilson

6 334          62     pet    F 41    170   Taylor

...

13 391          78         no pet   M 41    180 Singh

14 340          62        no pet   F 27    177 Singh

15 337          55         no pet   F 34    185 Singh

16 389          87         no pet   M 27    172 Campbell

17 376          78         no pet   F 33    167 Campbell

18 338          57         no pet   F 47    155 Li

19 337          62         no pet   M 50    172 Li

20 359          69         no pet   M 18    173 Li

> model<-lm(resp.flow~treatment+sex+age+height+body.weight)

> anova(model)

Analysis of Variance Table

Response: resp.flow

            Df Sum Sq Mean Sq F value    Pr(>F)   

Treatment    1     1.8     1.8   0.0569    0.8149   

sex          1 6626.9 6626.9 209.6419 8.117e-10 ***

age          1 10264.8 10264.8 324.7247 4.396e-11 ***

height       1 8346.9 8346.9 264.0536 1.758e-10 ***

body.weight 1 5786.0 5786.0 183.0373 1.978e-09 ***

Residuals   14   442.6    31.6                      

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

a) Identify three aspects of the design and/or analysis of this study that reduce your confidence in the conclusion that pets dont influence respiratory flow.    

b) List four assumptions of the model used in this analysis.

c) If the assumptions aren’t met, what are three approaches you can take to analyse the data?

d) Which variable in their analysis explained the most variance in respiratory flow?

e) In the ANOVA table below, which letters (A-E) represent numbers that would NOT change if the sample size of people increased?                      (1 mark)

Response: resp.flow

Df Sum Sq Mean Sq F value Pr(>F)   

Treatment    A            B             C            D                      E   

sex 1 6626.9 6626.9 209.6419 8.117e-10 ***

age 1 10264.8 10264.8 324.7247 4.396e-11 ***

height 1 8346.9 8346.9 264.0536 1.758e-10 ***

body.weight 1 5786.0 5786.0 183.0373 1.978e-09 ***

Residuals   14   442.6    31.6                      

Spring_Valley   AU_Park
1375            910
1399            935
1450            1160
1270            800
970             910
1350            1020
925             1020
875             860
1000            850
1120            873
1130            1300
1200            1100
830              795
1300            1220
1220            985
925             1060
885             1040
1560             925
1380            1450
1250            1350
900             1280
900             1160
1150             975
1440             950
930              795

A) Calculate the summary statistics for both Spring Valley and AU Park. Enter the values that you calculate into the table below. Report the values to 2 decimal places.

Summary Statistics:

B) What can you infer about the shape of the distribution of Spring Valley house prices by looking at the summary statistics you calculated in part c.

C) is there a difference in house prices in Spring Valley versus AU Park at α = 0.05.

(i) State the hypothesis that you want to test.

(ii) Record the value of the test statistic and its p-value.

(iii) What do you conclude for the test at α = 0.05?

D) Compute a 95% confidence interval for the difference in the mean house prices between Spring Valley and AU Park. Interpret your interval.

a recent study in compare the time spent together by a single and dual earner couples was 61 minutes per day, with a standard deviation of 15.5 minutes. for the Dual earner couples the mean number of minutes spent watching television was 48.4 minutes and a standard deviation of 18.1 minutes. at the 0.01 significant level we can conclude that the single earner couples on the average spend more time watching television together? there are 15 single earned and 12 dual earner couples studied. for calculation assume the single earner as the first sample

The random variable X ~ B(5, 0.8). Find the following using a Ti-83/84
a. Mean
b. Standard Deviation
c. P(3)
d. P(x > 3)

The Survey of Study Habits and Attitudes (SSHA) is a phychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200. The mean score for U.S. college students is about 115, and the standard deviation is about 30. A teacher who suspects that older students have better attitudes toward school gives that the SSHA to 25 students who are at least 30 years of age. Their mean is ¯x = 127.8.

(a) Assuming that σ = 30 for the population of older students, carry out a test of

H0 : µ = 115

Ha : µ > 115

Report the P-value of your test, and state your conclusion clearly.

(b) Your test in part (a) required two important assumptions in addition to the assumption that the value of σ is known. What are they? Which of these assumptions is most important to the validity of your conclusion in part (a)?

In a study of the effectiveness of a new pain killer, 46 out of 821 patients tested reported experiencing side effects. Use a a = 0.01 significance level to determine if the proportion who side effects from this drug is lower than the 7.8% rate of side effects for the older version of this medication.

I want to test the hypothesis that a die is fair by rolling it over and over, independently, until the third time I see any single number. I will conclude that the die is loaded (not fair) if it takes four or fewer rolls for any single number to come up three times.

What is the significance level?

Respond to the following in a minimum of 175 words, please type response:

Describe statistical inferences about two populations: How can comparisons be made for independent and dependent samples.

Respond to the following in a minimum of 175 words, please type response:

Describe analysis of variance & design of experiments: How does ANOVA extend the hypothesis testing analysis for two sample & more.

Respond to the following in a minimum of 175 words, please type response:

An important part of using statistics is being able to explain your results to decision makers. Imagine that you have conducted a two-sample test and determined that the difference was not statistically significant.   While one mean was 4.3 and the other was 3.9, the p level for the t test was p=.07. Your management team says, “Well, the difference may not be statistically significant, but the difference is there! Discuss how you would respond and how you would explain the purpose of the t test and significance in this case.

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 (BreakFast.xlsx)

(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?

The length of a species of fish is to be represented as a function of the age (measured in days) and water temperature (degrees Celsius). The fish are kept in tanks at 25, 27, 29 and 31 degrees Celsius. After birth, a test specimen is chosen at random every 14 days and its length measured.

Conceptional question: You need to answer my confusion other than just solving the problem. Better follow the comment

Q1. 10 students are divided into 5 groups and each group will be assigned a project topic

(a) if the 5 groups will work on 5 different topics, find the number of ways of forming groups (why I can't use the multinomial coefficient to calculate Question 1???????)

answer: 10C2*8C2*6C2*4C2*2C2=113, 400

Example: A police department in a small city consists of 10 officers. If the department policy is
to have 5 of the officers patrolling the streets, 2 of the officers working full time at the
station, and 3 of the officers on reserve at the station, how many different divisions
of the 10 officers into the 3 groups are possible?

Why I can use the multinomial coefficient to calculate this one? answer: 10!/(5!2!3!)

You decide to further your research project by hypothesizing that the true proportion of core body temperature increases amidst higher ambient temperature and humidity levels for the population who do not use electric fans is less than those who do use electric fans, setting the level of significance at 5% for the formal hypothesis test. In other words, you extend your sampling to two samples instead of just one. You randomly sample 31 and 39 participants for your first and second groups, respectively, based on your research funding and for 45 minutes, all study participants sit in a chamber maintained at a temperature of 108 degrees Fahrenheit (i.e., 42 degrees Celsius) and a relative humidity of 70%. After the first 45-minute warming period, you record the participants' core body temperatures. Furthermore, for Group 2 only you place a personal sized electric fan 3 feet away with its airflow directed at a given participant's chest area, and the participants relax in this position for the next 45 minutes, whereas for Group 1 you do not provide electric fans. At the end of this 45-minute fan period, you record the core body temperatures of all participants, documenting any temperature increases as compared to the start of the time period. The following table comprises the data you collect.

Per Step 3 of the 5-Steps to Hypothesis Testing, choose the appropriate decision rule.

Please note that 0 and 1 are defined as no and yes, respectively, which is a typical coding scheme in Public Health.

Select one:

a. Accept H₀ if t < -1.282

b. Reject H₀ if z ≤ -1.645

c. Reject H₀ if t = +1.282

d. Reject H₁ if z ≥ -2.326

**P.S: can you please explain how to get Z, and when to make it negative, i.e. why we choose upper tail and then make it - ? . Thanks alot