1) Golf-course designers have become concerned that old courses are becoming obsolete since new technology has given golfers the ability to hit the ball so far. Designers, therefore, have proposed that new golf courses need to be built expecting that the average golfer can hit the ball more than 255255 yards on average. Suppose a random sample of 135 golfers be chosen so that their mean driving distance is 252.5 yards. The population standard deviation is 42.6 Use a 5% significance level.

Calculate the followings for a hypothesis test where ?0:?=255: and ?1:?<255

(a)    The test statistic is    

(b)    The P-Value is

The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) ? and standard deviation ?=0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5 mg. Now, suppose a reporter wants to test whether the mean nicotine content is actually higher than advertised. He takes measurements from a SRS of 20 cigarettes of this brand. The sample yields an average of 1.45 mg of nicotine. Conduct a test using a significance level of ?=0.05

(a) The test statistic  

(b) The critical value, z* =

A random sample of 100 observations from a population with standard deviation 11.99 yielded a sample mean of 92.

1. Given that the null hypothesis is ?=90 and the alternative hypothesis is ?>90 using ?=.05α, find the following:

(a) Test statistic =
(b)  P - value:

Given that the null hypothesis is ?=90 and the alternative hypothesis is ?≠90 using ?=.05α, find the following:
(a) Test statistic ==  
(b)  P - value:

It is necessary for an automobile producer to estimate the number of miles per gallon achieved by its cars. Suppose that the sample mean for a random sample of 150 cars is 30.7 miles and assume the standard deviation is 2.1 miles. Now suppose the car producer wants to test the hypothesis that ? the mean number of miles per gallon, is 28 against the alternative hypothesis that it is not 28. Conduct a test using ?=.05 by giving the following:

(a)    positive critical ? score    

(b)    negative critical ? score    

(c)    test statistic

35 people are randomly selected and the accuracy of their wristwatches is checked, with positive errors representing watches that are ahead of the correct time and negative errors representing watches that are behind the correct time. The 35 values have a mean of 107sec and a standard deviation of 218sec. Use a 0.01significance level to test the claim that the population of all watches has a mean of 0 sec.

The test statistic is

The P-Value is

Given the significance level ?=0.07 find the following:

(a)    left-tailed ?z value
?=

(b)    right-tailed z value
?=

(c)    two-tailed ? value
|?|=

The city of​ Belgrade, Serbia, is contemplating building a second airport to relieve congestion at the main airport and is considering two potential​ sites, X and Y. Hard Rock Hotels would like to purchase land to build a hotel at the new airport. The value of land has been rising in anticipation and is expected to skyrocket once the city decides between sites X and Y.​ Consequently, Hard Rock would like to purchase land now. Hard Rock will sell the land if the city chooses not to locate the airport nearby. Hard Rock has four​ choices: (1) buy land at​ X, (2) buy land at​ Y, (3) buy land at both X and​ Y, or​ (4) do nothing. Hard Rock has collected the following data​ (which are in millions of​ euros):                                                                                       Site X Site Y Current purchase price 26 22 Profits if airport and hotel built at this site 50 40 Sale price if airport not built at this site 12 7 Hard Rock determines there is a 50​% chance the airport will be built at X​ (hence, a 50​% chance it will be built at​ Y).

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!')

Ti Fan and his wife have retired. They are touring the USA in a big recreational vehicle (RV). They are towing a Prius car, which they use for running errands when the RV is parked. However, towing the Prius decreases the gas mileage of the RV by 25%. Ti Fan wonders if they would save gas if his wife drives the Prius instead of towing it. The Prius gets good mileage, 50 miles per gallon. Ti Fan has never wanted to know the mileage of the RV, since it would be discouraging. Nonetheless, he looks at the odometer when he fills the RV's gas tank, then looks again when he fills it again. Towing the Prius, he drove 255 miles and burned 37 gallons of gas. How much would they save, in gallons, if they had travelled the 255 miles with his wife driving the Prius while Ti Fan drove the RV?

Volkswagen sells the "Golf" in both gasoline-powered and electric-powered versions. The gasoline Golf gets 37 miles/gallon and the electric e-Golf gets 3.42 miles/kWh. Assume the average person drives 12,000 miles per year.

a) What are the annual emissions in kg CO2 for driving the Golf and e-Golf? For gasoline, assume that it emits 8,165 g CO2 per gallon of gasoline. For electricity, use the table below to determine greenhouse gas emissions.

b) If the e-Golf cost $3,000 more than the gasoline Golf, what is the payback time for purchasing the e-Golf instead of the gasoline Golf. Assume the gasoline costs $3/gallon and electricity costs $ 0.10/kWh.

A statisitcs instructor participates in triathalons. the table lists the times in minutes and seconds, he recorded while riding five laps through each mile of a 3-mile loop. Use a .05 significance level to test the claim that is takes the same time to ride each of the miles.

Determine the null and alternate hypotheses.

Find the F statistic

P VALUE

What is the conlusion for this hypothesis test?

(fail to reject, reject) There is (sufficient, insufficient) evidence to warrant the rejection of the claime that the three different miles have the same mean ridetime.

Does one of the miles appear to have a hill?

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the original claim.

A shipping firm suspects that the mean life of a certain brand of tire used by its trucks is less than 33,000 miles. To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 32,250 miles with a standard deviation of 1200 miles. At α = 0.05, test the shipping firm's claim.


a) State the Null and alternative hypotheses   


b) Find the test statistic . (1 mark)  


c) Fine the critical value. ( 1 mark)


d) Draw a final conclusion that addresses the claim ( 2 marks)

The distance a vehicle travels can be calculated as follows:
Distance = Speed * Time
For example, if a train travels 40 miles-per-hour for three hours, the distance traveled is 120 miles. Write a program that asks for the speed of a vehicle (in miles-per-hour) and the number of hours it has traveled. Both values are assumed to be integers. It should use a
loop to display the distance a vehicle has traveled for each hour of a time period specified by the user. For example, if a vehicle is traveling at 40 mph for a three-hour time period, it should display a report similar to the one that follows:

Hours Distance Traveled
---------------------------
1 40
2 80
3 120

Do not accept a negative number for speed and do not accept any value less than 1 for time traveled.

Sample Run
java DistanceTravelled

Enter vehicle speed (in mph): 60↵
Enter time travelled (in hrs): 2↵
Hour→Distance Travelled↵
--------------------------↵
1→→60↵
2→→120↵

ASSIGNMENT 5 REQUIREMENTS

The distance a vehicle travels can be calculated as follows:

distance = speed * time

For example, if a train travels 40 miles per hour for 3 hours,

the distance traveled is 120 miles.

Write a program that asks the user for the speed of a vehicle

(in miles per hour) and how many hours it has traveled.

The program should then use a loop to display the distance the

vehicle has traveled for each hour of that time period.

Here is an example of the output:

What is the speed of the vehicle in mph? 40

How many hours has it traveled? 3

Hour Distance Traveled

--------------------------------

1. 40

2. 80

3. 120

Input Validation:

Do not accept a negative number for speed and

do not accept any value less than 1 for time traveled.

=================================================================

TEST SET

============================

TEST CASE SPEED HOURS

1. 55 12

2. 65 10

3. 75 8

----------------------------