Question No 4

1. Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0 for the level of significance α. (Marks 1.5)

Left -tailed test

z = -1.52

α = 0.04

2. A trucking firm suspects that the mean life of a certain tire it uses is less than 35,000 miles. To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 34,450 miles with a standard deviation of 1200 miles. At α = 0.05, test the trucking firmʹs claim. (Marks 2)

1. A SRS of 30 commuters to the Los Angeles metropolitan area are selected, and each is asked how far they commute to work each day. In the sample, the mean distance is 64 miles and the standard deviation is 12 miles. Is there evidence that the average commute to work for this population is more than 60 miles?

a. Yes, since the p-value is less than 0.05.

b. No, since the p-value is less than 0.05.

c. No, since the p-value is greater than 0.05.

d. Yes, since the p-value is greater than 0.05.

In the past few weeks we have learned that the number of miles driven has fallen due to people staying at home during the coronavirus pandemic. Insurers are offering auto insurance rebates to policyholders due to the decrease in number of miles driven. New research however indicates that this does not tell the entire driving story.

1. Although miles driven and traffic congestion are falling, both the accident rate and severity of accidents seems to be rising. Please explain what’s happening and why.  

What can be done to improve safety? Is it time to act to address this issue?

Bash Script

Write a script using while-do-done loop to convert the kilometers to miles.

- Ask the user to input the number of kilometers they need to travel.

- Display the number of equivalent miles for the number. Use formula, Kilometers = miles/0.62137

- Every time the loop runs, it should ask the user if they want to continue, if user enters “Y” or “y”, then the loop runs again, if user enters “N” or “n”, then stop the loop and print “Thank you for using this application”.

- If the user enters any other character, then display/print “Invalid entry” and break the loop.

A new van costs $25,000, has an estimated useful life of five years and an estimated salvage value of $5,000 at the end of that time. It is expected that the van will be driven 100,000 miles during its useful or service life.

The Nation Express Company purchases this van on April 1, 2019. During 2019 the van is driven 13,000 miles and during 2020 it was driven 21,000 miles. On January 1, 2021, the van is sold for $7,000.

Calculate the depreciation expense for 2019 and 2020 using:

1. Straight-line

2. Double-declining-balance

3. Units-of-production

mooth Riding Limo Company purchased a new limosine for $60,000 on April 30, 2016. The limo is expected to have a service life of 10 years or 110,000 miles and a residual value of $5,000. The limo was driven 12,000 miles in 2016 and 15,000 miles in 2017. Smooth Riding computes depreciation to the nearest whole month. Compute depreciation expense for 2016 and 2017 using the activity method Also, calculate the book value at the end of each year, 2016 and 2017. You must SHOW YOUR WORK! Points are given based on work shown and final answer.

The cost in dollars of operating a jet-powered commercial airplane Co is given by the following equation
Co = k*n*v^(3/2)
where
n is the trip length in miles,
v is the velocity in miles per hour, and
k is a constant of proportionality.
It is known that at 590 miles per hour the cost of operation is $300 per mile. The cost of passengers' time in dollars equals $226,000 times the number of hours of travel. The airline company wants to minimize the total cost of a trip which is equal to the cost of operating plus the cost of passengers' time.
At what velocity should the trip be planned to minimize the total cost?
HINT: If you are finding this difficult to solve, arbitrarily choose a number of miles for the trip length, but as you solve it, you should be able to see that the optimal velocity does not depend on the value of n​

Suppose your vehicle’s speedometer is geared to accurately give your speed only using a certain tire size: 17” diameter wheels (the metal part) and a 6.5” tires (thickness of rubber part).

a. If your vehicle’s instruments are properly calibrated, how many times should your tire rotate per second if you are travelling at 55 miles per hour?

b. Now find the angular speed from part a.

c. Suppose you bought new 7.1” tires for your 17” diameter wheels. You took the for a test run and drove at a constant speed of 55 miles per hour (according to your vehicle’s instrument). However, a law enforcement officer stopped you and claimed that you were speeding in a 55 miles per hour zone. How fast did the officer’s radar clock you at, in miles per hour?

The following table gives the total area in square miles​ (land and​ water) of seven states. Complete parts​ (a) through​ (c).

You are interested in finding a 98% confidence interval for the average commute that non-residential students have to their college. The data below show the number of commute miles for 10 randomly selected non-residential college students. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a

distribution.

b. With 98% confidence the population mean commute for non-residential college students is between and miles.

c. If many groups of 10 randomly selected non-residential college students are surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of commute miles and about percent will not contain the true population mean number of commute miles.