Module 2, Week 4, Paper and Pencil Assignment 4

 

Module 2, Week 4, Paper and Pencil Assignment 4

 

1. You have the following random samples containing information on annual income (measured in thousands) and marital status for individuals living in urban and rural areas.

 

Urban annual income	Urban Married	Rural annual income	Rural Married
33	Yes	22	Yes
56	Yes	81	Yes
88	No	19	No
43	No	26	Yes
28	Yes	38	Yes
42	Yes	101	No
105	No	31	Yes
90	Yes	29	No
21	Yes	35	Yes
47	No	39	Yes
57	No	66	Yes
19	No	99	No
118	Yes	18	Yes
77	Yes	92	Yes
50	Yes	65	Yes
31	No	48	No

 

The samples have the following standard deviations:

= 30.41            = 29.26

 

a)     Test the hypothesis that there is a difference in mean income between people living urban areas and rural areas. Use a 5% level of significance.

 

b)     Test the hypothesis that there is a difference in the proportion of people married between those living in urban areas and those living in rural areas. Use a 5% level of significance.

2. The following table shows the expected and observed distribution of bachelor’s degrees held among a random sample of 100 full-time employees at a financial services firm.

 

Degree	Expected	Observed
Business	40	45
Economics	20	15
Accounting/Finance	20	28
Mathematics	10	2
Other	10	10

 

Conduct a hypothesis test to determine if the observed distribution of degrees fits the expected distribution. Use a 5% level of significance.

           

 

3. The following table is a cross-tabulation of home ownership and location of residence.

 

	Own home	Do not own home
Urban	31	59
Rural	29	41

 

 

Conduct a hypothesis test to determine if home ownership and location of residence are independent random variables. Use a 5% level of significance.

4. You have the following random sample of the number of daily calls to police stations in the cities of Baltimore, Washington DC, and Pittsburgh.

 

Baltimore	Washington DC	Pittsburgh
862	555	755
766	664	763
608	610	802
911	709	712
980	612	765
888	589	679
812	649	789
678	700	714
765	707	599
709	579	671
808	622	683

 

a)     Test the hypothesis that the mean number of daily calls differs across the three cities. The total sum of squares (SST) is equal to 330,463.64. Use a 5% level of significance.

b)     What is the difference between ANOVA with two categories and a two-sample t-test for differences in means?