Answered: The bad debt ratio for a financial…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.4: Collecting Data

Problem 2E

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Question

The bad debt ratio for a financial institution is defined to be the dollar value of loans defaulted divided by the total dollar value of all loans made. Suppose that a random sample of sixty-five banks in Illinois is selected and that their bad debt ratios (recorded as a percentage) are presented in the sample.

Banking officials claim that the mean bad debt ratio for all Midwestern banks is 3.5 percent and that the mean bad debt ratio for Illinois banks is higher. What is the null hypothesis? What is the t-value?

bank	Bad Debt Ratio
1	3.38
2	5.15
3	4.63
4	9.69
5	8.32
6	3.58
7	5.9
8	7.33
9	6.28
10	6.87
11	3.93
12	5.76
13	3.98
14	3.66
15	7.46
16	5.59
17	6.39
18	6.49
19	2.31
20	7.84
21	9.2
22	4.64
23	5.38
24	4.23
25	7.12
26	3.48
27	2.87
28	4.59
29	7.43
30	8.34
31	5.15
32	5.84
33	4.95
34	5.6
35	7.52
36	5.23
37	7.88
38	8.86
39	4.42
40	6.64
41	9.25
42	6.53
43	5.35
44	6.04
45	5.19
46	2.87
47	2.91
48	1.77
49	2.34
50	4.22
51	3.2
52	3.14
53	2.86
54	4.05
55	2.01
56	3.42
57	4.38
58	3.1
59	1.76
60	3.16
61	4.06
62	4.21
63	2.16
64	2.76
65	2.46

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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