Zagat restaurant guides publish ratings of restaurants for many large cities around the world. The restaurants are rated on a 0 to 30 point scale based on quality of food, decor, service, and cost. Suppose the regression equation that predicts the cost of dinner using the rating of the quality of food for the restaurants in a particular city is (cost of dinner) = 4.201*(food quality) + 2.823. Interpret the slope.

Question 3 options:

Discuss most suitable research strategies to be used

College Graduation Rates. Data from the College Results Online website compared the 2011 graduation rate and median SAT score for 92 similar-sized public universities and colleges in the United States. The scatterplot below shows the relationship between these two variables along with the least squares fit. Round all calculated results to 4 decimal places.

1. The relationship between median SAT score and graduation rate is  ? positive negative ,  ? weak strong , and  ? linear non-linear .

2. The explanatory variable is  ? graduation rate median SAT college year  and the response variable is  ? graduation rate median SAT college year .

The summary statistics for graduation rate and median SAT score are listed below. The correlation between graduation rate and median SAT score is 0.655.

Median SAT score: mean = 1035.9, standard deviation = 79.3
Graduation rate: mean = 51.9, standard deviation = 14.5

3. The equation of the regression line is y =  +  x

4. Complete the following sentence to interpret the slope of the regression line:

An increase of  in Median SAT score corresponds to a/an  ? decrease increase  of  in Graduation Rate.

5. The recorded median SAT score for Northern Michigan University is 1032. Use the regression equation to estimate the graduation rate for Northern Michigan University.

6. The recorded graduation rate for Northern Michigan University is 47. Complete the following sentence.

The residual for Northern Michigan University is  . This means the graduation rate at Northern Michigan University is
A. higher than
B. the same as
C. lower than
the rate predicted by the regression model.

7. Stanford University (an elite private university in California not included in this data set) has a median SAT score of 1455. Would it be appropriate to use this linear model to predict the graduation rate for Stanford?

A. No, because 102.094% is too large to be a reasonable graduation rate, even for an elite university.
B. Yes, because 1455 is a reasonable median SAT score for an elite university.
C. No, because 1455 is beyond the range of the data used to build the regression model.

Best seller books the meaning for the number of weeks 15 best seller list 22 weeks the standard deviation is 6.17 weeks the meaning for the number of weeks 15 New York times hard cover nonfiction book spent on the list is 28 weeks the standard deviation is 13.2 weeks at a= 0.10 can we conclude that there is a difference in the mean times for the number of weeks the books were on the best seller list? Note: don’t use the P value method, use the five steps of hypothesis testing method! Please and thank you!

stats

Consider the following Two-(Independent) Sample setting: A farmer who own 200 cows wants to compare two different feeds 1 and 2. The farmer first did simple random selection of 11 cows from his herd. Then, farmer randomly assigned 6 of the 11 cows to get Trt A, leaving the other 5 to get Trt B. For the 6 Trt A cows, the average weight gain was +2.1, while the Std dev of their(6) weight gains was 0.8. For the 5 Trt B cows, the average weight gain was +1.7 , while the Std dev of the (5) weight gains was 0.4.   Utilizing Chpt 21's Option 2 (having dof for 2-sample t = min of n₁ - 1 , n₂ - 1), conduct a 95% C.I for the mean Trt A - Trt B weight gain difference over the herd (i.e. population of 200 cows). Also, perform a 2-sided test of hypothesis to see if one can declare a significant difference in the two feeds, at the critical p-value level (alpha) of 0.05.

Ian is testing to see if Irvinites eat more fruits and vegetables than the average American. Previous research indicates that Irvinites eat 5.8 servings per day. The national average is 4.6 with a standard deviation of three. How many people does Josh need in his sample to achieve a power of .80

Given a standard normal distribution, find the area under the curve which
lies
(i) to the left of z = 1.43;
(ii) to the right of z = -0.89;
(iii) between z = -2.16 and z = -0.65.

Given a standard normal distribution, find the value of k such that
(i) P(Z < k) = 0.0427
(ii) P(Z > k) = 0.2946
(iii) P(-0.93 < Z < k) = 0.7235

A shady broker offers a dubious investment opportunity. In week 0, he sells a $11,000 note promising to repay $11,500 in one week. In week 1, he sells two such notes and uses to proceeds to pay off the week 0 investor. In week 2, he sells 4 notes and pays off week one investors. Each week, he sells twice many notes as the week before and uses the proceeds to pay off last week’s investors. An investment scam of this sort is known as a Ponzi scheme. a) How many notes did the broker sell in week 10? b) What was the total number of notes sold by week 10? c) How much money was collected by week 10? d) How much money was paid out by week 10? e) In week 10, the broker took his profits and left the country. How much money was the loss of the investors? The table below will help you to organize your work. Complete the table and write a paragraph discussing the situation.

Interpret the meaning of the significant main effect(s) and interaction(s) – what do they mean or what do they tell you?

In San Francisco, a sample of 3,284 wireless routers showed that 1,182 used encryption (to prevent hackers from intercepting information). In Seattle, a sample of 1,900 wireless routers showed that 630 used encryption.

(a) Choose the appropriate hypotheses to test whether or not the population proportion of encryption is higher in San Francisco than Seattle. Assume π1 is the proportion for San Francisco and π2 for Seattle.

(b-1) Specify the decision rule at α = .01. (Round your answer to 3 decimal places.)

Reject the null hypothesis if z_calc > ???

(b-2) Find the test statistic z_calc. (Do not round the intermediate calculations and round x₁ and x₂ to the nearest whole number. Round your answer to 3 decimal places.)

A person has $20,000 to invest in four possible opportunities. Each opportunity will accept investments in $1,000 units, but only after the required minimum investment has been made.The minimums are $2, $2, $3 and $4 thousand, respectively. How many investment strategies are possible if: (a) An investment must be made in each opportunity? (b) Investment are made in at least three opportunities?

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x overbar​, is found to be 109​, and the sample standard​ deviation, s, is found to be 10.

​(a) Construct a 98​% confidence interval about mu if the sample​ size, n, is 18.

​(b) Construct a 98​% confidence interval about mu if the sample​ size, n, is 25. ​

(c) Construct a 99​% confidence interval about mu if the sample​ size, n, is 18.

​(d) Could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed?

Suppose every 10 times you cast your line into a lake you successfully get 3 fish. Assume you cast your line 100 times.

a) What is the probability of successfully catching exactly two fish in this experiment?

b) Calculate or approximate the probability that the number of fish you catch at least 5.

How effective is gastric bypass surgery in maintaining weight loss in extremely obese people? A study conducted found that 71% of an SRS of 437 subjects who had received gastric bypass surgery maintained at least a 20% weight loss six years after surgery.

1) Give a 90% confidence interval for the proportion of those receiving gastric bypass surgery that maintained at least a 20% weight loss six years after surgery. (Round your answers to four decimal places.)

Answer: _____ to _____

2) Interpret your interval in the context of the problem. (Round your answers to two decimal places.)

Answer: Based on this study, we estimate with 90% confidence that between _____ % and _____ % of all gastric bypass patients will maintain at least a 20% weight loss for six years after surgery.

1. If the normality assumption is met, but the equal variance assumption is not met, what alternative analysis could be used in place of the traditional F test for a one-way ANOVA design?

a. Kruskal-Wallis test. b. Welch test. c. Independent t-test. d. Friedman test

2. Which one of the following would be considered a non-parametric alternative to a one-way between subjects ANOVA?

  a. Kruskal-Wallis test. b. Welch test. c. Independent t-test. d. Friedman test

3. As you know, most statistical analyses come with assumptions. Use of repeated measures ANOVA has an assumption that is referred to as the sphericity assumption. What is the null hypothesis that is being tested when the Mauchly Test of Sphericity is used?

a. the variances for the differences are all equal. b. the population means are all equal c. the sample variances are all equal

(4. - 5.) Individuals diagnosed with depression volunteered to participate in a study investigating the effect of type of treatment on depression. All participants were considered to be moderately depressed at the beginning of the study. Participants were randomly assigned to receive one of four treatments: anti-depressant (AD), in-person psychotherapy (PSY), web-based therapy (WB), or placebo drug (PL). After a designated treatment period, depression level was measured using a standard depression measure (lower scores indicate less depression).

4. Being diligent, the researcher conducted tests of the assumptions prior to conducting the main analysis. The results of these tests are below. Based on the results of these tests, does it seem reasonable that the researcher moved forward with the analysis using a traditional F test for a one-way ANOVA?

Levene's Homogeneity Test

-----------------------------------------------   

data : depscore and treatment   

statistic : 1.11828

num df     : 3   

denum df   : 16   

p.value    : 0.3709916   

Result     : Variances are homogeneous.

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Shapiro-Wilk Normality Test

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data : depscore and treatment

Level Statistic p.value   Normality

1    AD 0.9899775 0.9796155 Not reject

2    PL 0.9733112 0.8960491 Not reject

3   PSY 0.9519245 0.7509285 Not reject

4    WB 0.9736478 0.8981076 Not reject

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a. No, the Levene test rejects the null hypothesis being tested and the Shapiro-Wilk test fails to reject; the normality assumption is met, but the homogeneity of variance assumption is not met. b. Yes, both of the tests presented failed to reject the null hypothesis being tested, suggesting that both the normality and homogeneity of variance assumptions are met. c. Yes, both of the tests presented reject the null hypothesis being tested suggesting that both the normality and homogeneity of variance assumptions are met. d. No, the Levene test rejects the null hypothesis being tested and the Shapiro-Wilk test fails to reject; the normality assumption is not met, but the homogeneity of variance assumption is met.

5. The results from the analysis of data for this study is presented below. Based on using a significance level of .05, was it appropriate for the researcher to conduct the post hoc tests that are presented?

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

treatment    3 343.0   114.3   4.949 0.0128 *

Residuals   16 369.6    23.1                

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Posthoc multiple comparisons of means : Tukey HSD

    95% family-wise confidence level

$treatment

diff    l wr.ci upr.ci pval   

PL-AD   7.2 -1.496747 15.896747 0.1239   

PSY-AD 6.2 -2.496747 14.896747 0.2150   

WB-AD 11.6 2.903253 20.296747 0.0074 **

PSY-PL -1.0 -9.696747 7.696747 0.9872   

WB-PL   4.4 -4.296747 13.096747 0.4899   

WB-PSY 5.4 -3.296747 14.096747 0.3197   

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

a. Yes, it was appropriate, the overall test was not statistically significant. b. No, it was not appropriate, the overall test was statistically significant. c. Yes, it was appropriate, the overall test was statistically significant. d. No, it was not appropriate, the overall test was not statistically significant.