Magic the Gathering is a popular card game. Cards can be land cards, or other cards. We consider a game with two

players. Each player has a deck of 40 cards. Each player shuffles their deck, then deals seven cards, called their hand.

(a) Assume that player one has 10 land cards in their deck and player two has 20. With what probability will each player

have four lands in their hand?

(b) Assume that player one has 10 land cards in their deck and player two has 20.With what probability will player one have

two lands and player two have three lands in hand?

(c) Assume that player one has 10 land cards in their deck and player two has 20. With what probability will player two

have more lands in hand than player one?

Please answer all questions and show working

Patients arrive at Max hospital for X-ray according to a Poisson process. There is an X-ray machine and arriving patients form a single line that feeds the X-ray machine in a first-come-first-served order. Past data show that the average wait for a patient is 30 minutes. The service time in the process takes, on an average, 10 minutes, exponentially distributed. a)Average number of patients in the system b)Average number of patients in the queue c)Average time a patient spends in the system d)What is the arrival rate? e)Probability that the server is idle f)Probability that there is at least one patient in the system g)Probability that there are less than or equal to 3 patients in the system h)Probability that there are 3 patients in the system i)Probability that there are more than or equal to 2 but less than or equal to 3 patients in the system

Give an example of omitted variable bias in a multiple linear regression model. Explain how you would figure out the probable direction of the bias even without collecting data on this omitted variable. [3 marks]

use any data and answers those questions There are several stores that or businesses that set these types of goals. Would this tell us an overall average? For example lets just say the sales goal is 100,000 a month, this month 98,000 is sold that is clearly less than the goal. However is that what the test tells us? Or does it look at a long term average over several months? Why is it valuable to know if the results are statistically signficant?

thank you

Did Sales Reach Target Value?

            Business requires careful planning because storing goods is associated with the additional costs. Thus, business sets monthly revenue goals, and understanding if the sales have reached the monthly revenue goal is important. Let us take a retail chain, and suppose they have monthly revenues of the stores, and a certain goal revenue.

            In this case, the four-step hypothesis testing is as follows:

1) The null hypothesis suggests that the mean stores sale does not significantly differ from the goal value. The alternate hypothesis is opposite to null and it suggests that the difference between the mean stores sales and goal value is significantly different (Triola, 2015).

2) The decision rule is set according to the significance level. For this case, we can set the significance level 0.1 because we do not require the highest precision. Thus, if the significance of the calculated t-value exceeds 0.1, we do not have enough evidence to reject the null hypothesis. Otherwise, we reject the null and accept the alternate hypothesis (Ott, Longnecker & Draper, 2016).

3) At this stage, we calculate the test statistics using mean value, goal revenue, standard deviation of the mean (s), and the number of observations (n):

                           t=(Mean-Goal)/s/square root of n

.

Also, we obtain the significance of this t-value from statistical tables or statistical software. Afterwards, we compare the value with the significance level (Triola, 2015).

            4) The final step is interpretation of the statistical test for the real life situation. If the test confirms the null hypothesis, this means that the mean stores sales are approximately equal to the goal value. If the null is rejected, then the store chain underperforms, which is an important information for the management (Black, 2017).

            Therefore, in this problem t-test was used as a support for the decision-making process in management. It provides a statistical background for sales analysis of the store chain and provides management with the valuable information about business (Black, 2017).

  There are several stores that or businesses that set these types of goals. Would this tell us an overall average? For example lets just say the sales goal is 100,000 a month, this month 98,000 is sold that is clearly less than the goal. However is that what the test tells us? Or does it look at a long term average over several months? Why is it valuable to know if the results are statistically signficant?

Give an example of an endogenous variable in a multiple regression model. Explain

Let us continue with analyses of data from the study of M Daviglus et al (N Engl J Med 1997) on the relationship of fish consumption with death from coronary heart disease (CHD) among 1,822 male employees of the Western Electric Company Hawthorne Works in Chicago who were followed for 30 years. we consider the 242 men who reported consumption of ≥ 35 g/day of fish at baseline. Among these 242 men, 46 died of CHD during follow-up.

a. Provide a point estimate and an appropriate 95% confidence interval for the 30- year risk (probability) of CHD death among employees who typically consume at least 35 g/day of fish. Additionally provide a brief interpretation of your confidence interval.

b. Perform a one-sample test to determine whether the 30-year risk (probability) of CHD death in those who consumed at least 35 g/day of fish is significantly different from 0.25. Make sure to specify your null and alternative hypotheses and give a brief conclusion.

Suppose a die is rolled six times and you need to find

a) The probability that at least two 4 come up

b) The probability that at least five 4's come up

Solve using the Binomial probability formula.

Assume that female students’ heights are normally distributed with a mean given by µ = 64.2 in. and a standard deviation given by σ =2.6 in.

a) If one female student is randomly selected, find the probability that her height is between 64.2 inches and 66.2 inches

b) If 25 female students are randomly selected, find the probability that they have a mean height between 64.2 inches and 66.2 inches

1.Why/When would you use a screening design?

2. What does an orthogonal design mean?

3.T or F: A 2-factor design is said to be balanced if each factor is run an unequal number of times at the high and low levels.

M12 Q21

Professor Gill has taught General Psychology for many years. During the semester, she gives three multiple-choice exams, each worth 100 points. At the end of the course, Dr. Gill gives a comprehensive final worth 200 points. Let x₁, x₂, and x₃ represent a student's scores on exams 1, 2, and 3, respectively. Let x₄ represent the student's score on the final exam. Last semester Dr. Gill had 25 students in her class. The student exam scores are shown below.

Since Professor Gill has not changed the course much from last semester to the present semester, the preceding data should be useful for constructing a regression model that describes this semester as well.

(a) Generate summary statistics, including the mean and standard deviation of each variable. Compute the coefficient of variation for each variable. (Use 2 decimal places.)

Relative to its mean, would you say that each exam had about the same spread of scores? Most professors do not wish to give an exam that is extremely easy or extremely hard. Would you say that all of the exams were about the same level of difficulty? (Consider both means and spread of test scores.)

No, the spread is different; Yes, the tests are about the same level of difficulty.

Yes, the spread is about the same; Yes, the tests are about the same level of difficulty.     

No, the spread is different; No, the tests have different levels of difficulty.

Yes, the spread is about the same; No, the tests have different levels of difficulty.

(b) For each pair of variables, generate the correlation coefficient r. Compute the corresponding coefficient of determination r². (Use 3 decimal places.)

Of the three exams 1, 2, and 3, which do you think had the most influence on the final exam 4? Although one exam had more influence on the final exam, did the other two exams still have a lot of influence on the final? Explain each answer.

Exam 3 because it has the highest correlation with Exam 4; No, the other 2 exams do not have a lot of influence because of their low correlations with exam 4.

Exam 2 because it has the lowest correlation with Exam 4; Yes, the other 2 exams still have a lot of influence because of their high correlations with exam 4.     

Exam 3 because it has the highest correlation with Exam 4; Yes, the other 2 exams still have a lot of influence because of their high correlations with exam 4.

Exam 1 because it has the highest correlation with Exam 4; Yes, the other 2 exams still have a lot of influence because of their high correlations with exam 4.

(c) Perform a regression analysis with x₄ as the response variable. Use x₁, x₂, and x₃ as explanatory variables. Look at the coefficient of multiple determination. What percentage of the variation in x₄ can be explained by the corresponding variations in x₁, x₂, and x₃ taken together? (Use 1 decimal place.)
%

(d) Write out the regression equation. (Use 2 decimal places.)

Explain how each coefficient can be thought of as a slope.

If we hold all other explanatory variables as fixed constants, then we can look at one coefficient as a "slope."

If we hold all explanatory variables as fixed constants, the intercept can be thought of as a "slope."     

If we look at all coefficients together, the sum of them can be thought of as the overall "slope" of the regression line.

If we look at all coefficients together, each one can be thought of as a "slope."

If a student were to study "extra hard" for exam 3 and increase his or her score on that exam by 13 points, what corresponding change would you expect on the final exam? (Assume that exams 1 and 2 remain "fixed" in their scores.) (Use 1 decimal place.)


(e) Test each coefficient in the regression equation to determine if it is zero or not zero. Use level of significance 5%. (Use 2 decimal places for t and 3 decimal places for the P-value.)

Conclusion

We reject all null hypotheses, there is insufficient evidence that β₁, β₂ and β₃ differ from 0.

We reject all null hypotheses, there is sufficient evidence that β₁, β₂ and β₃ differ from 0.     

We fail to reject all null hypotheses, there is sufficient evidence that β₁, β₂ and β₃ differ from 0.

We fail to reject all null hypotheses, there is insufficient evidence that β₁, β₂ and β₃ differ from 0.

Why would the outcome of each hypothesis test help us decide whether or not a given variable should be used in the regression equation?

If a coefficient is found to be not different from 0, then it contributes to the regression equation.

If a coefficient is found to be different from 0, then it does not contribute to the regression equation.     

If a coefficient is found to be not different from 0, then it does not contribute to the regression equation.

If a coefficient is found to be different from 0, then it contributes to the regression equation.

(f) Find a 90% confidence interval for each coefficient. (Use 2 decimal places.)

(g) This semester Susan has scores of 68, 72, and 75 on exams 1, 2, and 3, respectively. Make a prediction for Susan's score on the final exam and find a 90% confidence interval for your prediction (if your software supports prediction intervals). (Round all answers to nearest integer.)

a) An environmental conservation agency recently claimed that more than 30% of Canadian consumers have stopped buying a certain product because the manufacturing of the product pollutes the environment. You want to test this claim. To do so, you randomly select 980 Canadian consumers and find that 314 have stopped buying this product because of pollution concerns. At a = 0.05, can you support the agency’s claim?

*please round your p-hat to 4 decimals before substituting in the z-statistic formula*

b) Refer to question (b). Construct a confidence interval for the true proportion of Canadian consumers who have stopped buying the product at the following levels of confidence: i). 90% ii). 95%

part 1.
An independent measures study has df = 48. How many total participants were in the study?
a. 24
b. 46
c. 50
d. There is not enough information

part 2.

A commonly cited standard for one-way length (duration) of school bus rides for elementary school children is 30 minutes.

A local government office in a rural area conducts a study to determine if elementary schoolers in their district have a longer average one-way commute time. If they determine that the average commute time of students in their district is significantly higher than the commonly cited standard they will invest in increasing the number of school busses to help shorten commute time. What would a Type 2 error mean in this context?

a. The local government decides that the average commute time is 30 minutes.

b. The local government decides that the data provide convincing evidence of an average commute time higher than 30 minutes, when the true average commute time is in fact 30 minutes.

c. The local government decides that the data do not provide convincing evidence of an average commute time higher than 30 minutes, when the true average commute time is in fact higher than 30 minutes.

d. The local government decides that the data do not provide convincing evidence of an average commute time different than 30 minutes, when the true average commute time is in fact 30 minutes.

Consider the following hypothesis test: H0: μ = 15 Ha: μ ≠ 15 A sample of 50 provided a sample mean of 14.12. The population standard deviation is 4. a. Compute the value of the test statistic (to 2 decimals). b. What is the p-value (to 4 decimals)? c. Using α = .05, can it be concluded that the population mean is not equal to 15? Answer the next three questions using the critical value approach. d. Using α = .05, what are the critical values for the test statistic? (+ or -) e. State the rejection rule: Reject H0 if z is the lower critical value and is the upper critical value. f. Can it be concluded that the population mean is not equal to 15?