I need help with a Calculus question. All explanations and answers will be used to help me learn.

There will be 7 questions multiple choice and numerical answer. I only need final answers.

Review the slideshow assignment . After reviewing the slideshow, answer the two questions about ticket prices. Remember to type and save your assignment as a Microsoft Word document and show all your work.

10th edition of Probability and Statistical Inference do Exercises

8.6-1, 8.6-2, 8.6-10, 8.7-1, 8.7-4, 8.7-5.

8.6-1. A certain size of bag is designed to hold 25 pounds of potatoes. A farmer fills such bags in the field. Assume that the weight X of potatoes in a bag is N(μ, 9). We shall test the null hypothesis H0: μ = 25 against the alternative hypothesis H1: μ< 25. Let X1,X2,X3,X4 be a random sample of size 4 from this distribution, and let the critical region C for this test be defined by x ≤ 22.5, where x is the observed value of X.

(a) What is the power functionK(μ) of this test? In partic-ular, what is the significance level α = K(25) for your test?

(b) If the random sample of four bags of potatoes yielded the values x1 = 21.24, x2 = 24.81, x3 = 23.62, and

x4 = 26.82, would your test lead you to accept or reject H0?

(c) What is the p-value associated with x in part (b)?

8.6-2. Let X equal the number of milliliters of a liquid in a bottle that has a label volume of 350 ml. Assume that the distribution ofX is N(μ, 4). To test the null hypothesisH0: μ = 355 against the alternative hypothesis H1: μ< 355, let the critical region be defined by C ={x : x ≤ 354.05}, where x is the sample mean of the contents of a random sample of n = 12 bottles. (a) Find the power function K(μ) for this test. (b) What is the (approximate) significance level of the test?

(c) Find the values of K(354.05) and K(353.1), and sketch the graph of the power function.

(d) Use the following 12 observations to state your con-clusion from this test:

350 353 354 356 353 352 354 355 357 353 354 355

(e) What is the approximate p-value of the test?

8.6-10. Let X have a Bernoulli distribution with pmf f(x; p) = px(1 − p)1−x,

x = 0, 1, n 0 ≤ p ≤ 1.

We would like to test the null hypothesis H0: p ≤ 0.4 against the alternative hypothesis H1: p > 0.4. For the test statistic, use Y =

i=1 Xi,where X1,X2,…,Xn is a ran-dom sample of size n from this Bernoulli distribution. Let the critical region be of the form C ={y: y ≥ c}.

(a) Let n = 100. Onthe same set of axes, sketch the graphs of the power functions corresponding to the three crit-ical regions, C1 ={y : y ≥ 40}, C2 ={y : y ≥ 50},and C3 ={y : y ≥ 60}. Use the normal approximation to compute the probabilities.

(b) LetC ={y: y ≥ 0.45n}.On the same set of axes, sketch the graphs of the power functions corresponding to the three samples of sizes 10, 100, and 1000.

8.7-1. Let X1,X2,…,Xn be a random sample from a normal distribution N(μ, 64).

(a) Show that C ={(x1, x2,…, xn): x ≤ c} is a best critical region for testing H0: μ = 80 against H1: μ = 76.

(b) Find n and c so that α ≈ 0.05 and β ≈ 0.05.

8.7-4. Let X1,X2,…,Xn be a random sample of Bernoulli trials b(1, p).

(a) Show that a best critical region for testing H0: p = 0.9 against H1: p = 0.8 can be based on the statistic Y =

n Y = i=1 Xi,which is b(n, p).

(b) If C ={(x1, x2,…, xn): n

n i=1 xi ≤ n(0.85)} and i=1 Xi, find the value of n such that α = P[Y ≤

n(0.85); p = 0.9] ≈ 0.10. HINT: Use the normal approximation for the binomial distribution.

(c) What is the approximate value of β = P[Y > n(0.85); p = 0.8 ] for the test given in part (b)?

(d) Is the test of part (b) a uniformly most powerful test when the alternative hypothesis is H1: p < 0.9?

8.7-5. Let X1,X2,…,Xn be a random sample from the normal distribution N(μ, 36).

(a) Show that a uniformly most powerful critical region for testing H0: μ = 50 against H1: μ< 50 is given by C2 ={x: x ≤ c}.

(b) With this result and that of Example 8.7-4, argue that a uniformly most powerful test for testing H0: μ = 50 against H1: μ = 50 does not exist.

a : Assignment 12a: Missing Value Problems

Submission Instructions: Write your answers to the problems on paper and then scan or take photos of those pages. If there are multiple pages to your completed assignment, you must submit them as one multi-page document (pdf, docx, jpg, or png).

Directions: Complete each of the following. On each double number line, you may make as many extra pairs of quantities as you would like in order to find the quantities you are being asked to find. Partial credit will be given if enough work is shown to indicate some understanding of the solutions.

1. The Original Recipe for orange juice calls for mixing 6 cans of juice concentrate with 8 cans of water. Draw a double number line and use it to find the following quantities so that the flavor of the juice is the same as the Original Recipe.
   1. How many cans of juice concentrate should be mixed with 10 cups of water?
   2. How many cans of water should be mixed with 9 cups of juice concentrate?
2. In a local bakery, each cupcake costs the same amount regardless of how many are purchased. The sign in the bakery states that 12 cupcakes cost $30. Draw a double number line and use it to find the following quantities. Make sure you write the dollar amounts correctly. For example, $4.50 is correct but $4.5 is not a correct way to write money.
   1. How much do 15 cupcakes cost?
   2. If someone spent $45, how many cupcakes did that person buy?
3. Dale charges $30 for shoveling snow for 2.5 hours. He always charges the same rate. Draw a double number line and use it to find the following quantities.
   1. How much will Dale charge if he shovels snow for half an hour?
   2. If Dan charged $18, how many hours did he shovel snow?
4. On a map, 1 inch represents 2.5 miles. Draw a double number line and use it to find the following quantities.
   1. How many miles are represented by 3 inches on the map?
   2. How many inches on the map would be used to represent 22.5 miles?

A building casts a 103-foot shadow at the same time that a 32-foot flagpole casts a 34.5-foot shadow. How tall is the building? (Round your answer to the nearest tenth of a foot.)Assignment 12b: Using Strip Diagrams to Solve Ratio Problems

Submission Instructions: Write your answers to the problems on paper and then scan or take photos of those pages. If there are multiple pages to your completed assignment, you must submit them as one multi-page document (pdf, docx, jpg, or png).

Directions: Complete each of the following. Partial credit will be given if enough work is shown to indicate some understanding of the solutions.

1. “Two pints of red paint are mixed with 5 pints of white paint to make 7 pints of pink paint. Find the quantities requested below so that every combination of white and red paint produces the same shade of pink paint as that original mixture.” It is recommended you draw a strip diagram to represent this problem so that you can answer the two questions below.
   1. If 8 pints of red paint were put in the mixture, how many pints of pink paint were made?
   2. If there are 42 pints of pink paint, how many pints of white paint are in the mixture?
2. One piece of string was 56 inches long. It was cut into two pieces such that their lengths are in a ratio of 3:4. How long is the shorter piece of string?
   1. Draw a strip diagram to represent that problem.
   2. How long is the shorter piece of string?
3. There are 75 red and green apples for sale at a farmer’s fruit stand. There are 4 times as many red apples as green apples. How many more red apples than green apples are there?
   1. Draw a strip diagram to represent that problem.
   2. How many more red apples than green apples are there?
4. A grocery store has 176 bottles for sale in their beverage cooler. Three-fifths of the bottles are water and the rest are sodas. How many bottles of water are in the beverage cooler?
   1. Draw a strip diagram to represent that problem.
   2. How many bottles of water are in the beverage cooler?
5. Could the word problem in #4 above, with the exact numbers that are in the problem, be a real-life problem? Explain.