Question

4.25 The results of a survey home?" follow. have a asking, "Do you have a calculator and/or a computer in your Calculator Yes No Yes 46 3 49 No 11 1526 Computer 57 18 75 Is the variable "calculator" independent of the variable "computer"? Why or why not? 4.26 In a recent year, business failures in the United States numbered 83,384, according to Dun & Bradstreet. The construction industry accounted for 10,867 of these business failures. The South Atlantic states accounted for 8,010 of the business failures. Suppose that 1,258 of all business failures were construction businesses located in the South Atlantic states. A failed business is randomly selected from this list of business failures. a. What is the probability that the business is located in the South Atlantic states? b. What is the probability that the business is in the construction industry or located c. What is the probability that the business is in the construction industry if it is d. What is the probability that the business is located in the South Atlantic states if it e. What is the probability that the business is not located in the South Atlantic states f. Given that the business is a construction business, what is the probability that the in the South Atlantic states? known that the business is located in the South Atlantic states? is known that the business is a construction business? if it is known that the business is not a construction business? business is not located in the South Atlantic states?

Answer 1

4.25

Here we need to use chi square test of independence. Hypotheses are:

H0: The variables calculator and computer are independent.

Ha: The variables calculator and computer are not independent.

Expected frequencies will be calculated as follows:

Following table shows the expected frequencies:

Following table shows the calculations for chi square test statistics:

Following is the test statistics:

Σ(부)-24767

Degree of freedom: df =( number of rows -1)*(number of columns-1) = (2-1)*(2-1)=1

The p-value is: 0.0000

Since p-value is less than 0.05 so we can conclude that the variables calculator and computer are not independent.