I am getting problems with my calculations. For the first part of the question I got 68 when I try another calculation I got 1. One of the method used was Degree of freedom =(r-1)(c-1).
TABLE 12-7
The director of transportation of a large company is interested in the usage of her van pool. She considers her routes to be divided into local and non-local. She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes. She takes a sample of a day's riders and finds the following:
Male Female Total
Local 27 44 71
Non-Local 33 25 58
Total 60 69 129
She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
(a) Referring to Table 12-7, the test will involve ________ degree(s) of freedom.
A) 1
B) 59
C) 68
D) 128
(b) Referring to Table 12-7, the overall or average proportion of local riders is ________.
A) 1.00
A) 0.01
A) 0.5504
A) 0.55
A) 0.05
(c) Referring to Table 12-7, the expected cell frequency in the Male/Local cell is ________.
A) 33.02
A) 33.00
A) 0.300
A) 0.330
A) 3.302
X^2 = Σ [(O-E)^2/E]
Where O = Observed Frequency and E = Expected Frequency
E = (column total*row total)/grand total
(a) (2-1)(2-1) = ?
(b) Local total/grand total = ?
(c) E = ?
A)b
B)c
C)a
a) B
b) C
c) B
To answer your questions, let's go through each part step by step:
(a) The formula for calculating the degree(s) of freedom in a chi-square test is (r-1)(c-1), where r is the number of rows and c is the number of columns in the given table. Referring to Table 12-7, we can see that there are 2 rows and 2 columns: Local/Non-Local and Male/Female. Therefore, plugging in the values, the degree(s) of freedom will be (2-1)(2-1) = 1. So, the correct answer is (A) 1.
(b) To find the overall or average proportion of local riders, we need to sum up the local riders in each category (Male and Female) and divide it by the total number of riders. From Table 12-7, we can see that the total number of local riders is 71. The total number of riders, which is the sum of all the cells in the table, is 129. So, the overall proportion of local riders is 71/129 ≈ 0.5504. Therefore, the correct answer is (C) 0.5504.
(c) To find the expected cell frequency in a specific cell, we need to calculate the expected frequency for each cell in the table using the formula: (row total * column total) / grand total. Let's calculate the expected cell frequency for the Male/Local cell.
The row total for Local is 71, the column total for Male is 60, and the grand total is 129. Plugging in these values, we get (71 * 60) / 129 = 33.02. Therefore, the correct answer is (A) 33.02.
I hope this helps you understand how to approach these questions and solve similar problems in the future. If you have any more questions, feel free to ask!