A sociologist was hired by a large city hospital to investigate the relationship between the number of
unauthorized days that employees are absent per year and the distance (miles) between home and
work for the employees. A sample of 6 employees was chosen, and the following data were collected.
Distance to work (miles) 1 3 4 6 8 10
Number of days absent 8 5 8 7 6 3

e. Compute the correlation coefficient.
f. Conduct a t-test at a 0.05 level of significance to test for a significant relationship between
distance to work and number of days absent. State your conclusion.
g. Conduct an F-test at a 0.05 level of significance to test for a significant relationship between
distance to work and number of days absent. State your conclusion.
h. Did you get the same conclusion for the t-test and the F-test? Will this always be the case for a
test for significance of the relationship in a simple linear regression?

Question text

7-step Hypothesis Testing Problem

Complete the 7 steps in Excel and upload the file here

Two major automobile manufacturers have produced compact cars with the same size engines.We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles.A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance.The following data show the results of the test.

At the 0.05 level of significance, conduct a 7-step hypothesis test to determine whether there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles.

Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a seven-lap race) with a standard deviation of 2.28 seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps.

• Part (a)

  In words, define the random variable X.

  the time (in seconds) per lapthe time (in seconds) per race    the distance (in miles) of each racethe distance (in miles) of each lap

• Part (b)

  Give the distribution of X.
  X ~

• Part (c)

  Find the percent of her laps that are completed in less than 135 seconds. (Round your answer to two decimal places.)
  

• Part (d)

  The fastest 2% of her laps are under how many seconds? (Round your answer to two decimal places.)
  sec

• Part (e)

  Enter your answers to two decimal places.
  
  The middle 80% of her lap times are from  seconds to  seconds.

(1.)                Railroads no longer dominate the freight transportation market, but they still lead the market in terms of freight ton-miles. What factors contribute to their leadership in this area? Why is their share of the total expenditures for freight movement so small if they lead in freight ton-miles?

(3.) Explain the difference between intramodal and intermodal competition in the railroad industry. Which form of competition is most beneficial to shippers? Why?

(5.) What factors have contributed to the decline in the volume of higher- value freight by the railroads? What changes, if any, could the railroads make to attract back more higher value freight from motor carriers?

(7.) The railroad industry has developed a number of new types of equipment to replace the standard boxcar. What is the rationale supporting the diversification of equipment?

(9.) Discuss the major current issues facing the railroad industry. Select one of these major issues and present appropriate recommendations for resolving the issue.

1. Test the claim that the proportion of people who own cats is significantly different than 30% at the 0.2 significance level.
The null and alternative hypothesis would be:

a) H0:μ≤0.3
Ha:μ>0.3

b) H0:p≥0.3
Ha:p<0.3

c) H0:μ≥0.3
Ha:μ<0.3

d) H0:p≤0.3
Ha:p>0.3

e) H0:μ=0.3
Ha:μ≠0.3

f) H0:p=0.3
Ha:p≠0.3

The test is:

-left-tailed

-two-tailed

-right-tailed

Based on a sample of 400 people, 31% owned cats
The p-value is: ____? (to 2 decimals)

Based on this we:

• Reject the null hypothesis
• Fail to reject the null hypothesis

2. You wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01.
      Ho:μ=89.7
      Ha:μ≠89.7
You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=12 with mean M=93.7 and a standard deviation of SD=8.6

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value = ______?
The p-value is...

• less than (or equal to) αα
• greater than αα

This p-value leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 89.7.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 89.7.
• The sample data support the claim that the population mean is not equal to 89.7.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 89.7.

Say I want to generate random variables from the probability distribution

p={ 2-2x 0<x<1

0 . elsewhere

My scheme is to generate U's from [0,1],double them and plug them into the probability distribution. So U = 0.3 gives me p(0.6)=0.8 as random variable. Prove my idea is right or wrong.

Which of the following 1.0 L mixtures has the greatest buffering capacity?

A

0.1 M NH4Cl +0.2 M NH3

B

1.0 M NH4Cl + 0.1 M NH3

C

0.2 M NH4Cl +0.8 M NH3

D

1.0 M NH4Cl + 1.2 M NH3

Arrange the following mixtures of buffer solutions in an increasing order of their pH values.

Drag and drop to order

1

A

0.10 M KF/0.10 M HF

2

B

0.20 M KF/0.10 M HF

3

C

0.10 M KF/0.20 M HF

(b) (5 points) Calculate a 90% confidence interval for the difference between the mean diameter of the entire batch produced at plant B and the mean diameter of the entire batch produced at plant A. Write a sentence interpreting the confidence interval.

Ebling Inc. finances with 0.2 fraction debt, 0.1 fraction preferred and the remaining common stock. Ebeling's before-tax cost of debt is 0.05, it cost of preferred stock is 0.12, and its cost of common stock is 0.16. If Ebeling is subject to a 0.3 fraction corporate income tax, what is the company's Weighted Average Cost of Capital?

The CO2 content of the air in a 5000 cu ft room is 0.3 percent. Fresh air containing 0.1 percent CO2 is pumped into the room at teh rate of 1000 ft^3/min . A) find the percentage of CO2 in the room after 30 min. When will the CO2 content be 0.2 percent?   ANS) 0.10 percent and 3.47 minutes