Confidence intervals for standard deviation

Here is a link to a post about estimating sigmax using sx, n and the chi square table. The degrees of freedom will be n - 1.

Using the Consumer Price Index table

The Consumer Price Index

This week, students got a green handout sheet with the consumer price index number for the years 1950 to 2015.  The simplest way to use it goes as follows.

How did prices change from 1960 to 1980? We use the two CPI values.

CPI(1960) = 29.6
CPI(1980) = 82.4

82.4/29.6 = 2.78378.....

29.6/82.4 = .35922...

What these numbers mean is that on average, a $10 item in 1960 sold for 10*2.78378... = $27.84 in 1980, while a $10 item in 1980 would have sold for 10*.35922... = $3.59.

We can use this to figure out the cost of living increase in any given year by dividing the CPI for that year by the CPI for the previous year.  For example, the rate in 1975 would be

CPI(1975)/CPI(1974) = 53.8/49.3 = 1.09127789... This is 1 + rate, so rounded to the nearest tenth of a percent we would have 9.1% and to the nearest hundredth of a percent it would be 9.13%.

Let's look at the number CPI(1980)/CPI(1960) = 2.783783... This gives us how much prices increased in the 20 year period from 1961 to 1980. To get the average increase over those 20 years, we take (2.783783)^(1/20) = 1.05252... This is 1 + rate, so the average rate = .05252... or 5.3% if rounded to the nearest tenth of a percent and 5.25% rounded to the nearest hundredth.

Answers to Quiz 8

Here are the answers to Quiz 8, which will be counted as a lab instead of a quiz and a new Quiz 8 will be given on Tuesday, with checksums.

Data set: 1990-2009 n = 20

R² =.5956

yp = .1830x - 361.3035

What is the value of yp when you plug in 1990? 2.8665

What is the value of yp when you plug in 2009? 6.3435

95% confidence threshold = .1971 Does R² surpass it? Yes

99% confidence threshold = .3147 Does R² surpass it? Yes

====================


Data set: 1990-2009 n =10

R² =.1601

yp = .1006x -196.0848

What is the value of yp when you plug in 2000? 5.1152

What is the value of yp when you plug in 2009? 6.0206

95% confidence threshold = .3994 Does R² surpass it? No

99% confidence threshold = .5852 Does R² surpass it? No

Links to posts about chi square and goodness of fit

Here is a link to a post about the chi-square table.

Our first application will be goodness of fit.

The frequency table solution for TI-83 and TI-84

Put the list of numbers in one list (let's say L1) and the frequencies in a separate list (for simplicity's, make it L2 in this example.) Under the STAT menu, in the CALC sub-menu, choose

2-Var Stats L1, L2

Assuming the frequencies are in the second list, the sum of the y values is n, the size of the sample and the sum of the xy is the sum of all the x values. You then need to divide (sum of xy)/(sum of y) to get the average x-bar.

As for the median, you have to do it by hand, just like the folks with the TI-30xIIs.

Here are the lists from class, the first number x and the second number f(x). The answers are in the comments.

This year's daily differences, 2015 - (avg. 1999-2014)
-9, 1
-8, 3
-7, 4
-6, 7
-5, 13
-4, 15
-3, 12
-2, 16
-1, 11
0, 24
1, 27
2, 24
3, 24
4, 25
5, 18
6, 14
7, 11
8, 8
9, 14
10, 5
11, 7
12, 1
13, 1
14, 4
15, 2
16, 3
17, 5
18, 4
20, 2
21, 1

Here is the list of wins by NFL teams in 2014

12, 5
11, 4
10, 3
9, 4
8, 2
7, 4
6, 3
5, 1
4, 2
3, 2
2, 2

Answers in the comments.