Question

Use Minitab to answer the questions. Make sure to copy all output from the Minitab:

The U.S. Bureau of Labor Statistics publishes a variety of unemployment statistics, including the number of individuals who are unemployed and the mean length of time the individuals have been unemployed. For November 1998, the Bureau of Labor Statistics reported that the national mean length of time of unemployment was 14.5 weeks.

The mayor of Chicago has requested the study on the status of unemployment in City of Chicago. A sample of 60 unemployed residents shows the sample mean is 15.7 and the sample standard deviation is 9.0. Test whether the length of time in Chicago is long than national average.

1) Let's think about the house price. According to the Case-Shiller Home Price Indices in August 2009, Chicago and San Francisco have following sample mean and population standard deviations (the sample mean was calculated by daily base, so the sample size was 30):

	CHICAGO	San Francisco
Sample Mean	130.55	132.47
Population Standard Deviation	9	12

                  

Using hypothesis test, prove if these house price indices are same.  (Setup a hypothesis, show your works to perform the test, and state your verdict)

2)             Some people argue that San Francisco has higher house price than that of Chicago. Prove/disprove the argument using a hypothesis test.

3)             Let’s assume the population standard deviations are unknown, and the sample standard deviation of for Chicago is 9.2 and that of San Francisco is 11.5. Some people argue that San Francisco has higher variability (higher variance) in house prices than that of Chicago. Setup a hypothesis, perform the test and prove/disprove the argument.

4.     Let’s consider a company’s growth rate of sales.

Year	Annual Growth Rate (%)
1993	6.80
1994	6.10
1995	5.60
1996	5.40
1997	4.90
1998	4.50
1999	4.20
2000	4.00
2001	4.80
2002	5.80
2003	6.20
2004	5.50
2005	5.00
2006	6.10

Find the sample mean and sample standard deviation using Minitab using descriptive statistics.

The store manager found that the average growth rate in 80s was 6.00%. Using the data, prove if the average growth rate for the sample period was same as that of 80s.

Prove if the average growth rate was less than 6%.

Answer 1

1.

H0: the length of time in Chicago is long than national average
H1: the length of time in Chicago is not long than national average

Let the los be alpha = 5%

P-value = 0.153 > alpha 0.05 so we accept H0

Thus we conclude that  the length of time in Chicago is long than national average

2) a) H0: There is no significance difference between the means of CHICAGO and San Francisco

H1: There is significance difference between the means of CHICAGO and San Francisco

Let the los be alpha = 5%

Here P-value > alph a0.05 so we accept H0

Thus we conclude that there is no significance difference between the means of CHICAGO and San Francisco

b) H0: San Francisco has higher house price than that of Chicago

H1: San Francisco has not higher house price than that of Chicago

Here P-value > alph a0.05 so we accept H0

Thus we conclude that San Francisco has higher house price than that of Chicago

c)

H0: San Francisco has not higher variability (higher variance) in house prices than that of Chicago.

H1: San Francisco has higher variability (higher variance) in house prices than that of Chicago.

P-value > alpha 0.05 so we accept H0

thus we conclude that San Francisco has not higher variability (higher variance) in house prices than that of Chicago.