The average house has 10 paintings on its walls. Is the mean smaller for houses owned by teachers? The data show the results of a survey of 14 teachers who were asked how many paintings they have in their houses. Assume that the distribution of the population is normal.

7, 11, 8, 10, 10, 7, 7, 7, 11, 10, 7, 8, 10, 7

What can be concluded at the αα = 0.10 level of significance?

1. For this study, we should use Select an answer z-test for a population mean t-test for a population mean
2. The null and alternative hypotheses would be:

H0:H0:  ? μ p  Select an answer < > ≥ ≤ ≠ =       

H1:H1:  ? μ p  Select an answer < ≤ ≠ ≥ > =    

3. The test statistic ? t z  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? ≤ >  αα
6. Based on this, we should Select an answer fail to reject reject accept  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the population mean is not significantly less than 10 at αα = 0.10, so there is enough evidence to conclude that the population mean number of paintings that are in teachers' houses is equal to 10.
   • The data suggest the populaton mean is significantly less than 10 at αα = 0.10, so there is enough evidence to conclude that the population mean number of paintings that are in teachers' houses is less than 10.
   • The data suggest that the population mean number of paintings that are in teachers' houses is not significantly less than 10 at αα = 0.10, so there is not enough evidence to conclude that the population mean number of paintings that are in teachers' houses is less than 10.
8. Interpret the p-value in the context of the study.
   • If the population mean number of paintings that are in teachers' houses is 10 and if you survey another 14 teachers, then there would be a 0.32% chance that the population mean number of paintings that are in teachers' houses would be less than 10.
   • If the population mean number of paintings that are in teachers' houses is 10 and if you survey another 14 teachers, then there would be a 0.32% chance that the sample mean for these 14 teachers would be less than 8.57.
   • There is a 0.32% chance that the population mean number of paintings that are in teachers' houses is less than 10.
   • There is a 0.32% chance of a Type I error.
9. Interpret the level of significance in the context of the study.
   • If the population mean number of paintings that are in teachers' houses is less than 10 and if you survey another 14 teachers, then there would be a 10% chance that we would end up falsely concuding that the population mean number of paintings that are in teachers' houses is equal to 10.
   • If the population mean number of paintings that are in teachers' houses is 10 and if you survey another 14 teachers, then there would be a 10% chance that we would end up falsely concuding that the population mean number of paintings that are in teachers' houses is less than 10.
   • There is a 10% chance that teachers are so poor that they are all homeless.
   • There is a 10% chance that the population mean number of paintings that are in teachers' houses is less than 10.

2. The joint pmf of ? and ? is given by

??,? (?, ?) = （x+y）/27  ??? ? = 0, 1,2; ? = 1, 2, 3,

and ??,? (?, ?) = 0 otherwise.

a. Find ?(?|? = ?) for all ? = 0,1, 2.

b. Find ?(3 + 0.2?|? = 2).

Rolling a dice 15 times, find the probability of 6 consecutive rolls have 6 distinct numbers. (i.e. 423123456..., 45612335626..., etc.)

Give an example foe each of the following

1) R (Multiple R)

2) R^2 (Multiple R^2)

3) Zero-order correlation

4) partial correlation

5) shared variance

6) The Directionality Problem

7) The Third Variable Problem

8) Moderator variable

9) Mediator variable

Data from a sample of 10 pharmacies are used to examine the relationship between prescription sales volume and the percentage of prescription ingredients purchased directly from the supplier. The sample data is given below (Use formula to answer each question).

percent ingredient 10 18 25 40 50 63 42 30 5 55

sales volume in $1000 25 55 50 75 110 138 90 60 10 100

a. Draw scatter plot between percent ingredient (x-variable) and the sale volume (y variable). What can you say about the association between percent ingredient and the sale volume?

b. Calculate the mean and standard deviation for both predictor (% ingredient) and the response (sale volume) and sample correlation coefficient . ?

c. Use the information from part (a) above to determine the regression parameters (slope and intercept) using formula.

d. Interpret the slope in the context.ˆ

e. Write the equation of the regression line to predict sale volume from % ingredient

.f. Briefly describe goodness of fit of the fitted model that you have in part (d) above.g. Use the model to predict the sale volume when percent ingredient is 35%. Interpret the predicted value.

Are you more likely to purchase a brand mentioned by an athlete on a social media site? According to Catalyst Digital Fan Engagement survey, 53% of social media sports fans would make such a purchase.

A) Suppose that the survey had a sample size of n=500. Construct a 95% confidence interval estimate for the population proportion of social media sports fans that would more likely purchase a brand mentioned by an athlete on a social media site.

B) Based on (a), can you claim that more than half of all social media sports fans would more likely purchase a brand mentioned by an athlete on a social media site?

C) Repeat parts (a) and (b), assuming that the survey had a sample size of n=5,000.

D) Discuss the effect of sample size on confidence interval estimation.

Finally, the researcher considers using regression analysis to establish a linear relationship between the two variables – hours worked per week and income earned per year.

c) Estimate a simple linear regression model and present the estimated linear equation. Display the regression summary table and interpret the intercept and slope coefficient estimates of the linear model.                                                           

COIN TOSSES In a large class of introductory Statistics students, the professor has each student toss a coin 16 times and calculate the proportion of his or her tosses that were heads. The students then report their results, and the professor plots a histogram of these several proportions.

1. What shape would you expect this histogram to be? Why?

2. Where do you expect the histogram to be centred?

3. How much variability would you expect among these proportions?

4. Explain why a Normal model should not be used here.

The answer is

1, symmetric

2, 0.5

3, 0.125

4. np=8<10

Please explain why the third question has answer 0.125. how did you get it?

1 paragraph on why are z-scores so important in statistics?

Daniel measures the volume of several raindrops at Jonestown as 0.6 ml, 0.65 ml, 0.7 ml, 0.75 ml, 0.8 ml and 0.85 ml; and comes to believe that the raindrops at Jonestown are significantly larger than the national average of 0.65ml at the 5% level.

If daniel does the appropriate statistical test, what will be his conclusion?

1. Consider the following game: 3 players can contribute or not to a public good. For the public good to be successfully created, 2 contributions are necessary (a third contribution would not add anything to the public good).
   These are the payoffs each of the three players assign to all possible outcomes:

   3: I didn't contribute but the public good was created anyway 2: I did contribute and the public good was created
   1: I didn't contribute and the public good was not created
   0: I did contribute and the public good was not created

   The decisions are made sequentially: player 1 moves, then player 2, then player 3.

   (a) Find the set of pure strategy Nash equilibria of this game if it is played as a simultaneous move game.

   (b) Find the set of subgame perfect Nash equilibria of this game when it is played sequentially.

Waterbury Insurance Company wants to study the relationship between the amount of fire damage and the distance between the burning house and the nearest fire station. This information will be used in setting rates for insurance coverage. For a sample of 30 claims for the last year, the director of the actuarial department determined the distance from the fire station (x) and the amount of fire damage, in thousands of dollars (y). The MegaStat output is reported below

-1. Write out the regression equation. (Round your answers to 3 decimal places.) a-2. Is there a direct or indirect relationship between the distance from the fire station and the amount of fire damage? How much damage would you estimate for a fire 9 miles from the nearest fire station? (Round your answer to the nearest dollar amount.) c-1. Determine and interpret the coefficient of determination. (Round your answer to 3 decimal places.) c-2. Fill in the blank below. (Round your answer to one decimal place.) d-1. Determine the correlation coefficient. (Round your answer to 3 decimal places.) d-2. Choose the right option. d-3. How did you determine the sign of the correlation coefficient? e-1. State the decision rule for 0.01 significance level: H0 : ρ = 0; H1 : ρ ≠ 0. (Negative value should be indicated by a minus sign. Round your answers to 3 decimal places.) e-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.) e-3. Is there any significant relationship between the distance from the fire station and the amount of damage? Use the 0.01 significance level. rev: 10_12_2017_QC_CS-102203

The correlation coefficient r is a sample statistic. What does it tell us about the value of the population correlation coefficient ρ (Greek letter rho)? You do not know how to build the formal structure of hypothesis tests of ρ yet. However, there is a quick way to determine if the sample evidence based on ρ is strong enough to conclude that there is some population correlation between the variables. In other words, we can use the value of r to determine if ρ ≠ 0. We do this by comparing the value |r| to an entry in the correlation table. The value of α in the table gives us the probability of concluding that ρ ≠ 0 when, in fact, ρ = 0 and there is no population correlation. We have two choices for α: α = 0.05 or α = 0.01.

(a) Look at the data below regarding the variables x = age of a Shetland pony and y = weight of that pony. Is the value of |r| large enough to conclude that weight and age of Shetland ponies are correlated? Use α = 0.05. (Use 3 decimal places.)

(b) Look at the data below regarding the variables x = lowest barometric pressure as a cyclone approaches and y = maximum wind speed of the cyclone. Is the value of |r| large enough to conclude that lowest barometric pressure and wind speed of a cyclone are correlated? Use α = 0.01. (Use 3 decimal places.)

1. For the data below perform a Wilcoxon Rank-Sum Test by-hand showing all steps (you may verify your results using software if you want to but it’s not required).
   Two treatments were developed for asthma patients. Twelve patients were randomly assigned to one of Treatment A or Treatment B (six patients on each treatment). The response variable is the number of days that the patients were symptom free after using their assigned treatments for a week. Test to see if Treatment A has a distribution that is shifted to the right (i.e. tends to have larger values) than Treatment B.
   Show all steps of your test and use 5% level of significance.