In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at row B, the annual company percentage increase in revenue, versus row A, the CEO's annual percentage salary increase in that same company. Suppose a random sample of companies yielded the following data:

B: Percent increase for company 26,25,27, 18, 6, 4, 21, 37

A: Percent increase for CEO 25, 25, 22, 14, −4, 19, 15, 30

Level of significance is 5%

a) What is the value of the sample test statistic? (Round your answer to three decimal places.)

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below.

Level of significance is 1%

b) What is the value of the sample test statistic? (Round your answer to three decimal places.)

A) In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

B)

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

Do professional golfers play better in their last round? Let row B represent the score in the fourth (and final) round, and let row A represent the score in the first round of a professional golf tournament. A random sample of finalists in the British Open gave the following data for their first and last rounds in the tournament.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below.

Does this information indicate that the peak wind gusts are higher in January than in April? Use α = 0.01. (Let

d = January − April.)(a) What is the level of significance?


State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

H₀: μ_d = 0; H₁: μ_d ≠ 0; two-tailed H₀: μ_d = 0; H₁: μ_d > 0; right-tailed     H₀: μ_d = 0; H₁: μ_d < 0; left-tailed H₀: μ_d > 0; H₁: μ_d = 0; right-tailed

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal. We assume that d has an approximately uniform distribution. The Student's t. We assume that d has an approximately uniform distribution.     The standard normal. We assume that d has an approximately normal distribution. The Student's t. We assume that d has an approximately normal distribution.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

Can the italicized portion of the problem be explained? I understand up until the 0.015 moles of protonated acetic acid remained and I understand the HH portion of the problem after but I would like some clarity on how this number was concluded.

2. The following question has two parts.
a) What is the final pH of a solution obtained by mixing 250 ml of 0.3 M acetic acid with 300 ml

of 0.2 M KOH? (pKb of acetate = 9.24). (Show your work!)

Moles of acetic acid = 0.25 l X 0.3 M = 0.075 moles
Adding 0.3 l X 0.2 M = 0.06 moles of OH- to this solution will convert 0.06 moles of acetic

acid to 0.06 moles of acetate, 0.015 moles of protonated acetic acid will remain. pKa = 14 - pKb = 14 - 9.24 = 4.76

pH = pKa + log [CH3CO2-][CH3CO2H]

= 4.76 + log 0.06 moles / 0.55 l 0.015 moles / 0.55 l

= 4.76 + log 0.06 moles0.015 moles

= 5.36

pH = 5.36

An organization collected preference ratings on various brands they consider.

7.15 Channel equalization. We suppose that u1, . . . , um is a signal (time series) that is trans- mitted (for example by radio). A receiver receives the signal y = c ∗ u, where the n-vector c is called the channel impulse response. In most applications n is small, e.g., under 10, and m is much larger. An equalizer is a k-vector h that satisfies h∗c ≈ e1, the first unit vector of length n + k − 1. The receiver equalizes the received signal y by convolving it with the equalizer to obtain z = h ∗ y.

(a) How are z (the equalized received signal) and u (the original transmitted signal) related? Hint. Recall that h∗(c∗u) = (h∗c)∗u.

(b) Numerical example. Generate a signal u of length m = 50, with each entry a random value that is either −1 or +1. Plot u and y = c ∗ u, with c = (1,0.7,−0.3). Also plot the equalized signal z = h ∗ y, with

h = (0.9, −0.5, 0.5, −0.4, 0.3, −0.3, 0.2, −0.1).

1. I need to fuel my car every week. Based on my observation, the price of gas really follows a Markov Chain. The price can be 3.2 dollars, 3.3 dollars or 3.4 dollars for one gallon. If the price for this week is 3.2 dollars, the price of next week will be 3.2, 3.3 and 3.4 with the probability of 0.4, 0.4 and 0.2 respectively. If the price for this week is 3.3 dollars, the price of next week will be 3.2, 3.3 and 3.4 with the probability for 0.2, 0.5 and 0.3 respectively. If the price for this week is 3.4 dollars, the price of next week will be 3.2, 3.3 and 3.4 with probability 0.3, 0.3 and 0.4 respectively.
   1. Please give out the transition matrix.
   2. For one year, how much should I pay for the gas for my car? (Assume 52 weeks/year and I use 10 gallons every week).
   3. If the price of this week is 3.2 dollars, what is the probability that I will observe 3.3 dollars price after 2 weeks?

If the price of this week is 3.2 dollars, I will observe 3.3 dollars price for the first time after how many weeks in average?

1)What is z0 if

P(z > z₀) = 0.12

P(z < z₀) = 0.2

P(z > z₀) = 0.25

P(z < z₀) = 0.3

For this portion of the lab, you will reuse the Python program you wrote before.
That means you will open the lab you wrote in the previous assignment and change it. You should NOT start from scratch. Also, all the requirements/prohibitions from the previous lab MUST also be included /omitted from this lab.   
Redesign the solution so that some portions of the code are repeated. In lab 4 you validated input to ensure that the user entered inputs within certain values. If the user entered an invalid value, the program terminated. Now you will add a loop such that the user gets three chances to enter a valid value. If the user enters an invalid value more than three times in a row, the program should issue an error message and terminate.

The program I wrote before is shown below.

How can I apply the new requirements to reuse this program?

#Get a value from user.
Miles = float(input('How many miles would you like to convert into kilometers: '))

#Condition
if Miles >= 0:

#Convert miles to kilomters
Kilometers = Miles * 1.6

#Display result
print(Miles,"miles is equal to", Kilometers,"kilometers.")

#Get a value from user.
Gallons = float(input('How many gallons would you like to convert into liters: '))

#Condition
if Gallons >= 0:

#Convert gallons to liters
Liters = Gallons * 3.9

#Display result
print(Gallons,"gallons is equal to", Liters,"liters.")

#Get a value from user.
Pounds = float(input('How many pounds would you like to convert into kilograms: '))

#Condition
if Pounds >= 0:

#Convert pounds to kilograms
Kilograms = Pounds * 0.45

   #Display result

   print(Pounds,"pounds is equal to", Kilograms,"kilograms.")

#Get a value from user.
Inches = float(input('How many inches would you like to convert into centimeters: '))

#Condition
if Inches > 0:
  
#Convert inches to centimeters
Centimeters = Inches * 2.54

#Display result
print(Inches,"inches is equal to",Centimeters,"centimeters.")

#Get a value from user.
Fahrenheit = float(input('How many fahrenheit would you like to convert into celsius: '))

#Condition   
if Fahrenheit < 1000:

#Convert fahrenheits to celsius
Celsius =(Fahrenheit - 32) * 5/9

#Display result
print(Fahrenheit,"fahrenheits is equal to",Celsius,"celsius.")

else:
#Display error message
print('Invalid value!')

else:
#Display error message
print('Invalid value!')

else:
#Display error message

else:
#Display error message
print('Invalid value!')

else:

#Display error message
print('Invalid value!')