Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows: x 1 2 3 4 p(x) .4 .3 .2 .1

a. Consider a random sample of size n = 2 (two customers), and let X be the sample mean number of packages shipped. Obtain the probability distribution of X .

b. Refer to part (a) and calculate P (Xbar is less than or equal to 2.5)

c. Again consider a random sample of size n = 2, but now focus on the statistic R = the sample range (difference between the largest and smallest values in the sample). Obtain the distribution of R.

d. If a random sample of size n = 4 is selected, what is p (Xbar less than or equal to 1.5)?

1. The grades on a chemistry midterm at Springer are roughly symmetric with μ=67 and σ=2.0. William scored 66 on the exam.

1. Find the z-score for William's exam grade. Round to two decimal places.
2. What percentage of students in this midterm scored less than William?
3. What percentage of students scored more than 70 in this midterm?

2. The grades on a language midterm at Oak are roughly symmetric with μ=67 and σ=2.5. Ishaan scored 70 on the exam.

1. Find the z-score for Ishaan's exam grade. Round to two decimal places.
2. What percentage of students in this midterm scored less than Ishaan?
3. What percentage of students scored more than 70 in this midterm?

3. The grades on a math midterm at Springer are roughly symmetric with μ=78 and σ=5.0. Omar scored 70 on the exam.

1. Find the z-score for Omar's exam grade. Round to two decimal places.
2. What percentage of students in this midterm scored less than Omar?
3. What percentage of students scored more than 80 in this midterm?
4. What percentage of students scored between 70 and 90 in this midterm?

4. The grades on a geometry midterm at Springer are roughly symmetric with μ=68 and σ=2.0. Emily scored 69 on the exam.

1. Find the z-score for Emily's exam grade. Round to two decimal places.
2. What percentage of students in this midterm scored less than Emily?
3. What percentage of students scored more than 75 in this midterm?
4. What percentage of students scored between 65 and 75 in this midterm?

The accompanying data represent the total travel tax​ (in dollars) for a​ 3-day business trip in 8 randomly selected cities. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outliers. Complete parts​ (a) through​ (c) below. 68.12 79.32 68.56 84.72 79.34 86.19 100.95 98.55 LOADING... Click the icon to view the table of critical​ t-values. ​(a) Determine a point estimate for the population mean travel tax. A point estimate for the population mean travel tax is ​$ nothing. ​(Round to two decimal places as​ needed.) ​(b) Construct and interpret a 95​% confidence interval for the mean tax paid for a​ three-day business trip. Select the correct choice below and fill in the answer boxes to complete your choice. ​(Round to two decimal places as​ needed.) A. One can be nothing​% confident that the all cities have a travel tax between ​$ nothing and ​$ nothing. B. The travel tax is between ​$ nothing and ​$ nothing for nothing​% of all cities. C. There is a nothing​% probability that the mean travel tax for all cities is between ​$ nothing and ​$ nothing. D. One can be nothing​% confident that the mean travel tax for all cities is between ​$ nothing and  ​$ nothing. ​(c) What would you recommend to a researcher who wants to increase the precision of the​ interval, but does not have access to additional​ data? A. The researcher could decrease the level of confidence. B. The researcher could increase the level of confidence. C. The researcher could decrease the sample standard deviation. D. The researcher could increase the sample mean. Click to select your answer(s).

The data set mantel in the alr4 package has a response Y and three predictors x1, x2 and x3.

(a) Apply the forward selection and backward elimination algorithms, using AIC as a criterion function. Report your findings.

(b) Use regsubsets() function in R to determine the best model. Which appear to be the important predictors? What’s the final model? Explain your reasoning.

Jacob Jones is the manager of the produce section at Snell’s grocery store. Jacob must determine each day how many pounds of bananas to order from the supplier. Demand varies somewhat from day to day and if Jacob orders too many bananas, he will have to sell leftovers at a discount, if he orders too few bananas, customers will be dissatisfied and complain to his boss.   Jacob wants to set up a profit model in Excel to experiment with the number of pounds of bananas he should order each day.

Bananas are ordered (and assume delivered the same day) from the supplier each day and cost Jacob 15 cents per pound. They are sold for 69 cents a pound if sold the first day after delivery.  

Any bananas that are not sold the first day must be discounted to 39 cents per pound. Assume all bananas that are discounted will be sold at the lower price.

a. Set up an EXCEL spreadsheet in order to calculate profit for Jacob’s banana problem.

First day Demand and Order Quantity are separate unknown variables.  

You must use the Excel IF function in this model.

b. Using Excel Data/What-If/Data Table create a two way-table to show how profit changes with changes in First day demand and Quantity ordered. Use values of 100, 120, 140, 160, 180, and 200 for both variables in your table.

The better-selling candies are often high in calories. Assume that the following data show the calorie content from samples of M&M's, Kit Kat, and Milky Way II.

Assuming we don't know about the shape of the population distribution, use the Kruskal-Wallis Test to test for significant differences among the calorie content of these three candies.

State the null and alternative hypotheses.

H₀: Median_MM = Median_KK = Median_MW
H_a: Median_MM ≠ Median_KK ≠ Median_MW

H₀: Median_MM ≠ Median_KK ≠ Median_MW
H_a: Median_MM = Median_KK = Median_MW    

H₀: All populations of calories are identical.
H_a: Not all populations of calories are identical.

H₀: Median_MM = Median_KK = Median_MW
H_a: Median_MM > Median_KK > Median_MW

H₀: Not all populations of calories are identical.
H_a: All populations of calories are identical.

Find the value of the test statistic. (Round your answer to two decimal places.)

=

Find the p-value. (Round your answer to three decimal places.)

p-value =

At a 0.05 level of significance, what is your conclusion?

Reject H₀. There is not sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies

.Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.     

Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.

Reject H₀. There is sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.

difference between stem and leaf plot and dot plot? pros and cons of each one

As part of a​ survey, a marketing representative asks a random sample of 29 business owners how much they would be willing to pay for a website for their company. She finds that the sample standard deviation is​ $3419. Assume the sample is taken from a normally distributed population. Construct 99​% confidence intervals for​ (a) the population variance σ2 and​ (b) the population standard deviation σ. Interpret the results.

​(a) The confidence interval for the population variance is (___​,___​). ​(Round to the nearest integer as​ needed.)

Interpret the results. Select the correct choice below and fill in the answer​ box(es) to complete your choice. ​(Round to the nearest integer as​ needed.)

A.With 99​% ​confidence, you can say that the population variance is between ___ and ___.

B.With 1​% ​confidence, you can say that the population variance is greater than ___.

C.With 99​% ​confidence, you can say that the population variance is less than ___.

D.With 1​% ​confidence, you can say that the population variance is between ___ and ___.

​(b) The confidence interval for the population standard deviation is (___​,___​). (Round to the nearest integer as​ needed.)

Interpret the results. Select the correct choice below and fill in the answer​ box(es) to complete your choice. ​(Round to the nearest integer as​ needed.)

A.With 1​% ​confidence, you can say that the population standard deviation is less than ​$___.

B.With 99​% ​confidence, you can say that the population standard deviation is greater than ​$___.

C.With 1​% ​confidence, you can say that the population standard deviation is between ​$___ and ​$___.

D.With 99​% ​confidence, you can say that the population standard deviation is between ​$___ and ​$___.

The following table contains results from the regression of sales price (y) on lot size (x₁), number of bedrooms (x₂), number of bathrooms(x₃) and number of storeys (x₄). Sales price is the dependent variable and x₁,x₂,x₃,x₄ are independent variables.

R² = 0.54

F= stat = 48.3235

p value and F - stat of 1.18E - 88

n > 30.

a. Write down the least square prediction equation

b.use R² to check the validity of the model.

c use " t-stat" to check the validity of the coefficient at 5 % sig. level

d.use P value to check the validity of the coefficient at 1% sig level

e verbally explain each coefficient

f. check the validity of the model at 5% sig level ( use F stat and its P value )

Forgetting about the actual procedures, give me an example of real-world research question that would

(a) use a one-sample t-test

(b) use a two-sample t-test

Two types of medication for hives are being tested. The manufacturer claims that the new medication B is more effective than the standard medication A and undertakes a comparison to determine if medication B produces relief for a higher proportion of adult patients within a 30-minute time window. 20 out of a random sample of 200 adults given medication A still had hives 30 minutes after taking the medication. 12 out of another random sample of 200 adults given medication B still had hives 30 minutes after taking the medication. The hypothesis test is to be carried out at a 1% level of significance.

State the null and alternative hypotheses in words and in statistical symbols. (3 points)
What statistical test is appropriate to use? Explain the rationale for your answer. (3 points)
Would the test be right-tailed, left-tailed or two-tailed? Explain the rationale for your answer. (3 points)
Describe an outcome that would result in a Type I error. Explain the rationale for your answer. (3 points)
Describe an outcome that would result in a Type II error. Explain the rationale for your answer. (3 points)

a research center base in Canada used data sample of 25 university that over degree programme to investigate the nature of relationship between annual salaries of graduates Y and annual tuition fees X of these institutions .all measured in thousand of dollar per year . Preliminary analysis of the sample data produced the following sample information. summation Y=1034.97, summation Y^2 = 45237.19, summation X=528.599, summation X^2 = 11432.92 ,summation XY = 22250.54, n = 25. Use the above information to obtain the ordinary least square (OLS) estimate b1 cal and b2 cal and interpret the estimated equation of the regression line

Suppose seafood price and quantity data for the years 2000 and 2009 follow. Use 2000 as the base period.

(a)

Compute the index number (price relative) for each type of seafood. (Round your answers to one decimal place.)

(b)

Compute a weighted aggregate price index for the seafood catch. (Round your answer to one decimal place.)

I₂₀₀₉ =

Comment on the change in seafood prices over the nine-year period. (Enter your percentage as a positive value. Round your answer to one decimal place.)

Seafood prices have  ---Select--- increased decreased by  % over the 9-year period according to the index.

Graphically solve the following problem. You need not show me the graph. However, you would need to draw one to solve the problem correctly. You would need to indicate all the corner points clearly. Solve mathematically to identify the intersection points.

Maximize profit = 8 x1 + 5x2   

Subject to   

x1 + x2 <=10
x1 <= 6

x1, x2 >= 0

a. What is the optimal solution?

(You may utilize QM for Windows to answer b to d)
b. Change the right-hand side of constraint 1 to 11 (instead of 10) and resolve the problem. How much did the profit increase as a result of this?

c. Change the right-hand side of constraint 1 to 6 (instead of 10) and resolve the problem. How much did the profit decrease as a result? Looking at the graph, what would happen if the right-hand-side value were to go below 6?

d. Change the right-hand side of constraint 1 to 5 (instead of 10) and resolve the problem. How much did the profit decrease from the original amojnt as a result of this?

e. Examine the following output from QM. What is the dual price of constraint 1? What is the lower bound on this?

Ranging

f. What conclusions can you draw from this regarding bounds of the right-hand-side values and the dual price?

You have two coins, one of which you know to be fair and the other of which has a probability of turning up heads of 0.7, but you can’t tell which one is which. You choose one coin at random and flip it ten times getting an equal number of heads and tails. What is the probability that you chose the unfair coin?